Finite Group Databasebeta

← Group #13168758

Character table — Group #13168758

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order1222333666666666333466666666612121212121212122244121212123666121212121212121212224466666612121212121212121212121212121212446666666661212124444412121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-11-1111111111111-1-11111111111-11-1-1-11111-1-1-1-1-1-11-1-1-11111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-11-1-1111-1-1-1-11-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-11-11-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111-1-11111111111111111111-1111-1-1-1-1-1-11111111111111111-1-11-1111-1-1-1-11111-11-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111-1-11111111111111111111-1-11-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-11-1-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1111-1-1-1-1111-1-1-11-1-1-11111-1-1-111
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-111-1-1-1-11111-1-1-1-1111-111111-1-1-1-1-111-1-1-1-1-111-1-11-11-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-111-1-1111111-1-1-1-111-1-1-1-1-111-1-1111-1-11-111111-1-1-11-11-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-111-1-1-1-1-1-11111-1-11-111111-1-1-1-1-1-1111-1-1-1-1-11111-11-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-11111-1-111-1-11-11
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111-1-111-1-1-11-1-11111-1-111-1-111-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-11-1-1-1-1-111111-1111-1-1-1-1-11111-1-11
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-111-1-111-1-111-1-1-1-1-1-111111111111-1-111-1-1-1-1-11-111111-1-1-11-1-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-1-111-1-111-1-11111-1-1-1-1111111-11-1-1-1-1-11111111-1-1-1-1-111-1-11-111-1
χ17222222-1-12222-12-122-1-12-1-1-12-1-122-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-122022222-1-1000000-1-100000000002-1-1-1-1-1-1-1-12-1-102002-1-10000-10000
χ18222222-1-12222-12-122-1-12-1-1-12-1-122-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-12-20-22222-1-1000000110000000000-2-1111-1-1-1-1-2110-200-211000010000
χ19222222-1-12222-12-122-1-12-1-1-12-1-122-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2202-2-2-2-211000000-1-1000000000021-1-1-111112-1-10-200-211000010000
χ20222222-1-12222-12-122-1-12-1-1-12-1-122-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20-2-2-2-2-211000000110000000000-211111111-21102002-1-10000-10000
χ21222222-1-12222-12-122-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-222000000-1-1-1-1111111111-220-222-2-2-1-100000011000000000021-1-1-1-1-111-2110200-2110000-10000
χ22222222-1-12222-12-122-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-222000000-1-1-1-1111111111-2-20222-2-2-1-1000000-1-10000000000-21111-1-1112-1-10-2002-1-1000010000
χ23222222-1-12222-12-122-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-1111111111220-2-2-222110000001100000000002-1-1-1-111-1-1-2110-2002-1-1000010000
χ24222222-1-12222-12-122-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-11111111112-202-2-22211000000-1-10000000000-2-111111-1-12-1-10200-2110000-10000
χ2522222-122-1-122222-1-12-122-1-1-12-1-1-12-1-122-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-12020-1-1-1-122-1-1222200-1-1-1-1-1-1-1-12202000-1-1-1-10000002000-1-1-1-100000
χ2622222-122-1-122222-1-12-122-1-1-12-1-1-12-1-122-1-1-1-122-2-21111-1-1-1-1222-1-1-1-1-1-120-20-1-1-1-12211-2-2-2-20011111111-2-202000-1-1-1-1000000-2000111100000
χ2722222-122-1-122222-1-12-122-1-1-12-1-1-12-1-122-1-1-1-1-2-222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-20201111-2-2-1-1222200-1-1-1-1-1-1-1-1-2-20-20001111000000-2000111100000
χ2822222-122-1-122222-1-12-122-1-1-12-1-1-12-1-122-1-1-1-1-2-2-2-21111-1-1-1-1222-1-1-1-1-1-1-20-201111-2-211-2-2-2-20011111111220-200011110000002000-1-1-1-100000
χ2922222-122-1-122222-1-12-1-22-1-1-12-1-1-1211-2-211112222-1-1-1-1-1-1-1-1-2-2-2111111-20-20-1-111221122-2-200-1-1-1-11111220-2000-1-111000000-2000-1-11100000
χ3022222-122-1-122222-1-12-1-22-1-1-12-1-1-1211-2-2111122-2-21111-1-1-1-1-2-2-2111111-2020-1-11122-1-1-2-222001111-1-1-1-1-2-20-2000-1-111000000200011-1-100000
χ3122222-122-1-122222-1-12-1-22-1-1-12-1-1-1211-2-21111-2-222-1-1-1-1-1-1-1-1-2-2-211111120-2011-1-1-2-21122-2-200-1-1-1-11111-2-20200011-1-1000000200011-1-100000
χ3222222-122-1-122222-1-12-1-22-1-1-12-1-1-1211-2-21111-2-2-2-21111-1-1-1-1-2-2-2111111202011-1-1-2-2-1-1-2-222001111-1-1-1-1220200011-1-1000000-2000-1-11100000
χ332222-122222-1-12-122-1-122-122-1-12-1-1-122-1-1-1-1-1-100222222-1-1-1-12-1-122-1-1-1-1022200000022-1-1-1-122-1-1-1-1-1-1-1-100-102-1-10000-1-1-1202000000000-1-100
χ342222-122222-1-12-122-1-122-122-1-12-1-1-122-1-1-1-1-1-100222222-1-1-1-12-1-122-1-1-1-10-22-200000022-1-1-1-1-2-2-1-1-1-1-1-1-1-10010-2110000111-20-20000000001100
χ352222-122222-1-12-122-1-122-122-1-12-1-1-122-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-102-22000000-2-21111221111111100-102-1-10000-1-1-1-20-20000000001100
χ362222-122222-1-12-122-1-122-122-1-12-1-1-122-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-10-2-2-2000000-2-21111-2-2111111110010-2110000111202000000000-1-100
χ372222-122222-1-12-122-1-12-2-122-1-12-1-1-1-2-211111100222222-1-1-1-1-211-2-2111102-2-2000000-2-2-1-111-2-2-1-1-1-1111100-102-1-1000011120-20000000001-100
χ382222-122222-1-12-122-1-12-2-122-1-12-1-1-1-2-211111100222222-1-1-1-1-211-2-211110-2-22000000-2-2-1-11122-1-1-1-111110010-2110000-1-1-1-202000000000-1100
χ392222-122222-1-12-122-1-12-2-122-1-12-1-1-1-2-211111100-2-2-2-2-2-2-1-1-1-1-211-2-21111022-20000002211-1-1-2-21111-1-1-1-100-102-1-10000111-202000000000-1100
χ402222-122222-1-12-122-1-12-2-122-1-12-1-1-1-2-211111100-2-2-2-2-2-2-1-1-1-1-211-2-211110-2220000002211-1-1221111-1-1-1-10010-2110000-1-1-120-20000000001-100
χ412-22-2222-22-2-222-2-2-22220-2-2-2222-2-2-2000000002-22i−2i2i2i−2i−2i2-2-2200000000000002-2002-2002i−2i00002i2i−2i−2i00002i−2i000002-20000000000002i−2i0000000
χ422-22-2222-22-2-222-2-2-22220-2-2-2222-2-2-2000000002-2−2i2i−2i−2i2i2i2-2-2200000000000002-2002-200−2i2i0000−2i−2i2i2i0000−2i2i000002-2000000000000−2i2i0000000
χ432-22-2222-22-2-222-2-2-22220-2-2-2222-2-2-200000000-222i−2i2i2i−2i−2i2-2-220000000000000-2200-22002i−2i00002i2i−2i−2i0000−2i2i00000-22000000000000−2i2i0000000
χ442-22-2222-22-2-222-2-2-22220-2-2-2222-2-2-200000000-22−2i2i−2i−2i2i2i2-2-220000000000000-2200-2200−2i2i0000−2i−2i2i2i00002i−2i00000-220000000000002i−2i0000000
χ452-22-22-12-2-11-222-2-21-12-10-211-12-111-2−i3i300−i3−i3i3i32-22i−2i−i−iii-111-1000−i3i3−i3−i3i3i30000-11−i3i32-23−32i−2i0000−i−iii33−3−32i−2i00000-11−i3i30000000000−ii3−300000
χ462-22-22-12-2-11-222-2-21-12-10-211-12-111-2−i3i300−i3−i3i3i32-2−2i2iii−i−i-111-1000−i3i3−i3−i3i3i30000-11−i3i32-2−33−2i2i0000ii−i−i−3−333−2i2i00000-11−i3i30000000000i−i−3300000
χ472-22-22-12-2-11-222-2-21-12-10-211-12-111-2−i3i300−i3−i3i3i3-222i−2i−i−iii-111-1000−i3i3−i3−i3i3i300001-1i3−i3-223−32i−2i0000−i−iii33−3−3−2i2i000001-1i3−i30000000000i−i−3300000
χ482-22-22-12-2-11-222-2-21-12-10-211-12-111-2−i3i300−i3−i3i3i3-22−2i2iii−i−i-111-1000−i3i3−i3−i3i3i300001-1i3−i3-22−33−2i2i0000ii−i−i−3−3332i−2i000001-1i3−i30000000000−ii3−300000
χ492-22-22-12-2-11-222-2-21-12-10-211-12-111-2i3−i300i3i3−i3−i32-22i−2i−i−iii-111-1000i3−i3i3i3−i3−i30000-11i3−i32-2−332i−2i0000−i−iii−3−3332i−2i00000-11i3−i30000000000−ii−3300000
χ502-22-22-12-2-11-222-2-21-12-10-211-12-111-2i3−i300i3i3−i3−i32-2−2i2iii−i−i-111-1000i3−i3i3i3−i3−i30000-11i3−i32-23−3−2i2i0000ii−i−i33−3−3−2i2i00000-11i3−i30000000000i−i3−300000
χ512-22-22-12-2-11-222-2-21-12-10-211-12-111-2i3−i300i3i3−i3−i3-222i−2i−i−iii-111-1000i3−i3i3i3−i3−i300001-1−i3i3-22−332i−2i0000−i−iii−3−333−2i2i000001-1−i3i30000000000i−i3−300000
χ522-22-22-12-2-11-222-2-21-12-10-211-12-111-2i3−i300i3i3−i3−i3-22−2i2iii−i−i-111-1000i3−i3i3i3−i3−i300001-1−i3i3-223−3−2i2i0000ii−i−i33−3−32i−2i000001-1−i3i30000000000−ii−3300000
χ5344444-2-2-2-2-244-24-2-2-2-214-211-2-21-2-2-2-2-244-2-2-2-2440000001111-2-2-21111114000-2-2-2-2-2-20000000000000000000-200011110000000000000000000
χ5444444-2-2-2-2-244-24-2-2-2-214-211-2-21-2-2-2-2-244-2-2-2-2-4-40000001111-2-2-2111111-400022222200000000000000000002000-1-1-1-10000000000000000000
χ5544444-2-2-2-2-244-24-2-2-2-21-4-211-2-21-2-2-222-4-42222440000001111222-1-1-1-1-1-1-4000-2-222-2-20000000000000000000200011-1-10000000000000000000
χ5644444-2-2-2-2-244-24-2-2-2-21-4-211-2-21-2-2-222-4-42222-4-40000001111222-1-1-1-1-1-1400022-2-2220000000000000000000-2000-1-1110000000000000000000
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χ594444-24-2-244-2-2-2-2-24-21-2-41-2-2-21-2-2-21-4-42222220000000011112-1-122-1-1-1-1040-4000000000000220000000000-20-21100002-1-10000000000000000
χ604444-24-2-244-2-2-2-2-24-21-2-41-2-2-21-2-2-21-4-42222220000000011112-1-122-1-1-1-10-404000000000000-2-20000000000202-1-10000-2110000000000000000
χ614444-2-244-2-2-2-24-24-21-2-24-2-2-21-2-211-2-2-2-2-211110044-2-2-2-211114-2-2-2-211110040000000-2-2-2-2-2-20011111111000000000000000000000000000000
χ624444-2-244-2-2-2-24-24-21-2-24-2-2-21-2-211-2-2-2-2-2111100-4-4222211114-2-2-2-2111100-4000000022222200-1-1-1-1-1-1-1-1000000000000000000000000000000
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χ7644-4-4-2-2442-222-4-2-421-2-20-2-22-1221-120023−23−33−33000023−2323−2311-1-1023−2300−33−33000000000000000000−33−333-33-3000000000000000000000000000000
χ7744-4-4-2-2442-222-4-2-421-2-20-2-22-1221-120023−23−33−330000−2323−232311-1-1023−2300−33−330000000000000000003−33−3-33-33000000000000000000000000000000
χ7844-4-4-2-2442-222-4-2-421-2-20-2-22-1221-1200−23233−33−3000023−2323−2311-1-10−2323003−33−3000000000000000000−33−33-33-33000000000000000000000000000000
χ7944-4-4-2-2442-222-4-2-421-2-20-2-22-1221-1200−23233−33−30000−2323−232311-1-10−2323003−33−30000000000000000003−33−33-33-3000000000000000000000000000000
χ804-44-444-224-4-44-2-42-44-2-202224-2-2-4-42000000004-4000000-222-200000000000004-400-2200000000000000000000000-22000000000000000000000
χ814-44-444-224-4-44-2-42-44-2-202224-2-2-4-4200000000-44000000-222-20000000000000-44002-2000000000000000000000002-2000000000000000000000
χ824-44-44-2-22-22-44-2-422-2-2102-1-1-2-21222−2i32i300−2i3−2i32i32i34-40000001-1-11000i3−i3i3i3−i3−i30000-22−2i32i3-22000000000000000000000001-1i3−i30000000000000000000
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χ844-44-44-2-22-22-44-2-422-2-2102-1-1-2-212222i3−2i3002i32i3−2i3−2i34-40000001-1-11000−i3i3−i3−i3i3i30000-222i3−2i3-22000000000000000000000001-1−i3i30000000000000000000
χ854-44-44-2-22-22-44-2-422-2-2102-1-1-2-212222i3−2i3002i32i3−2i3−2i3-440000001-1-11000−i3i3−i3−i3i3i300002-2−2i32i32-200000000000000000000000-11i3−i30000000000000000000
χ864-44-4-244-44-42-242-4-4-2-2402-4-4-2-2422200000000004i−4i4i4i−4i−4i-222-2000000000000000000000−2i2i0000−2i−2i2i2i0000000000000000000000000000000000
χ874-44-4-244-44-42-242-4-4-2-2402-4-4-2-242220000000000−4i4i−4i−4i4i4i-222-20000000000000000000002i−2i00002i2i−2i−2i0000000000000000000000000000000000
χ884-44-4-2-24-4-222-242-421-2-202221-2-2-1-12−2i32i300i3i3−i3−i3004i−4i−2i−2i2i2i1-1-11000−2i32i3i3i3−i3−i3000000000023−23−2i2i0000ii−i−i−3−333000000000000000000000000000000
χ894-44-4-2-24-4-222-242-421-2-202221-2-2-1-12−2i32i300i3i3−i3−i300−4i4i2i2i−2i−2i1-1-11000−2i32i3i3i3−i3−i30000000000−23232i−2i0000−i−iii33−3−3000000000000000000000000000000
χ904-44-4-2-24-4-222-242-421-2-202221-2-2-1-122i3−2i300−i3−i3i3i3004i−4i−2i−2i2i2i1-1-110002i3−2i3−i3−i3i3i30000000000−2323−2i2i0000ii−i−i33−3−3000000000000000000000000000000
χ914-44-4-2-24-4-222-242-421-2-202221-2-2-1-122i3−2i300−i3−i3i3i300−4i4i2i2i−2i−2i1-1-110002i3−2i3−i3−i3i3i3000000000023−232i−2i0000−i−iii−3−333000000000000000000000000000000
χ924-4-44444-4-4-44-4-4-4444440-4-44-4-4-4-44400000000000000004-44-400000000000000000000000000000000000000000000000000000000000000000
χ934-4-4444-22-4-44-42-4-244-2-2022-2-422-44-20000000000000000-22-22000000000000000000000000000000000000000000000000000000−2i32i3000000000
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χ964-4-444-24-4224-4-4-44-2-24-20-42-22-422-240000000000002i3−2i3−2i32i3-22-220000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ974-4-44-244-4-4-4-22-4244-2-2402-4422-42-2-20000000000000000-22-220000000000000000000000023−2300000023−23−2323000000000000000000000000000000
χ984-4-44-244-4-4-4-22-4244-2-2402-4422-42-2-20000000000000000-22-2200000000000000000000000−2323000000−232323−23000000000000000000000000000000
χ994-4-44-2-24-422-22-424-21-2-2022-2-122-11-200003i−3i−3i3i0000−2i32i32i3−2i31-11-1000003i−3i−3i3i00000000000000−232300i3−i3−i3i33−3−33000000000000000000000000000000
χ1004-4-44-2-24-422-22-424-21-2-2022-2-122-11-200003i−3i−3i3i00002i3−2i3−2i32i31-11-1000003i−3i−3i3i0000000000000023−2300−i3i3i3−i3−333−3000000000000000000000000000000
χ1014-4-44-2-24-422-22-424-21-2-2022-2-122-11-20000−3i3i3i−3i0000−2i32i32i3−2i31-11-100000−3i3i3i−3i0000000000000023−2300i3−i3−i3i3−333−3000000000000000000000000000000
χ1024-4-44-2-24-422-22-424-21-2-2022-2-122-11-20000−3i3i3i−3i00002i3−2i3−2i32i31-11-100000−3i3i3i−3i00000000000000−232300−i3i3i3−i33−3−33000000000000000000000000000000
χ1038888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-4222200000000-1-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ1048888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-200000000-1-1-1-14-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ10588-8-88-4-4-44-4-8-84844-4-420-42-244-2-444000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4-44-4444-444222022-2-2-2-22-2-20043−43−2323−232300000000-1-1110−2323003−33−300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-4-44-4444-444222022-2-2-2-22-2-200−434323−2323−2300000000-1-111023−2300−33−3300000000000000000000000000000000000000000000000000000000
χ1088-88-8-48-448-84-4-444-8-42-40-244-42-444-200000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-44-444-4-44442220-2-2-2222-2-2-2−4i34i3002i32i3−2i3−2i300000000-111-10002i3−2i3−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-44-444-4-44442220-2-2-2222-2-2-24i3−4i300−2i3−2i32i32i300000000-111-1000−2i32i3i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ1118-8-888-4-44448-84-8-4-4-4-4204-2244-24-4-400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-48-44-8-8-4444-48-42-40-24-44-244-4200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4444-4444-4-42220-2-22-2-2-2-22200006i−6i−6i6i00000000-11-1100000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4444-4444-4-42220-2-22-2-2-2-2220000−6i6i6i−6i00000000-11-11000003i−3i−3i3i00000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).