Finite Group Databasebeta

← Group #13168183

Character table — Group #13168183

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order1222333666666666333466666666612121212121212122244121212123666121212121212121212244466666666666612121212121212121212446612121212121212121212244441212121212126121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1111111111111111-1-111111111111-1-1-111-1-1-1-1-11-1-1-11111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-1111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111-11-1-1-1-1-1-1111-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-1-1-11-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111-1-11111111111111111111111-111-1-111-1-11111-1-111111111-1-1-1-1-1111-1-11111-1-1-111-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111-1-111111111111111111111-1-1-111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1111-1-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1111-1-11111-11-1-1-11111-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-1-1-1111111111111-11-1-1-1-111-1-1-1-111-1-1-11111-11-1-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1111-1-1-11-1-111-1-11-111-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1111111111111-1-111-1-1-1-1-1-1-1-111-11-1-1-1-111-1-1-111-1111-1-111-1-111-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-11-111-1-1-1-111-1-11
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-111-11-111-1-1-1-111-11-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-11111-1-111-111-1111-1-111-1-11-11
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1111-1-111-1-111111111-1-1-1-1-1-111-1-111-1-11111-1-11-1-1-11-1-111-1-11-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11111-1-111-1-1111111-1-1-1-1-1-1-1-111-1-11-11111-1-111-1-111-1-1-11111-11-11-1
χ17222222-12-12-1222-12-12-12-122-1-1-1-12-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-10222002200-1-1000022-1-100000000-1-1-122-1-1-1-1-1-1-1202000000-1-1-10000
χ18222222-12-12-1222-12-12-12-122-1-1-1-12-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-10-2-22002200-1-10000221100000000-1-1-1-2-21-1-11111-20-20000001110000
χ19222222-12-12-1222-12-12-12-122-1-1-1-12-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1022-200-2-200110000-2-2-1-10000000011122-111-1-1-1-1-20-20000001110000
χ20222222-12-12-1222-12-12-12-122-1-1-1-12-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-10-2-2-200-2-200110000-2-21100000000111-2-21111111202000000-1-1-10000
χ21222222-12-12-1222-12-12-1-2-122-1-1-1-12-1-2-2-2-2-2-2-2-222000000-1-1-1-111111111102-2-2002200-1-10000-2-2-1-100000000-1-112-2111-1-111-202000000-1-110000
χ22222222-12-12-1222-12-12-1-2-122-1-1-1-12-1-2-2-2-2-2-2-2-222000000-1-1-1-11111111110-22-2002200-1-10000-2-21100000000-1-11-22-11111-1-120-200000011-10000
χ23222222-12-12-1222-12-12-1-2-122-1-1-1-12-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-111111111102-2200-2-20011000022-1-10000000011-12-21-1-1-1-11120-200000011-10000
χ24222222-12-12-1222-12-12-1-2-122-1-1-1-12-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-11111111110-22200-2-20011000022110000000011-1-22-1-1-111-1-1-202000000-1-110000
χ2522222-1222-122-1-1222-1-122-1-1-12-1-1-12-1-122-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1200222-1-1-1-122-1-1-1-1-1-10022-1-1-1-122-1-12000-1-1000002000-1-1-1-10000000
χ2622222-1222-122-1-1222-1-122-1-1-12-1-1-12-1-122-1-1-1-122-2-21111-1-1-1-1222-1-1-1-1-1-1-2002-2-2-1-111221111-1-100-2-21111-2-2-1-12000-1-100000-200011110000000
χ2722222-1222-122-1-1222-1-122-1-1-12-1-1-12-1-122-1-1-1-1-2-222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1200-22211-1-1-2-2-1-1-1-1110022-1-1-1-1-2-211-20001100000-200011110000000
χ2822222-1222-122-1-1222-1-122-1-1-12-1-1-12-1-122-1-1-1-1-2-2-2-21111-1-1-1-1222-1-1-1-1-1-1-200-2-2-21111-2-211111100-2-211112211-200011000002000-1-1-1-10000000
χ2922222-1222-122-1-1222-1-1-22-1-1-12-1-1-1211-2-211112222-1-1-1-1-1-1-1-1-2-2-2111111-200-2-2-2-1-111221111110022-1-1-1-122-1-1-20001100000-200011-1-10000000
χ3022222-1222-122-1-1222-1-1-22-1-1-12-1-1-1211-2-2111122-2-21111-1-1-1-1-2-2-2111111200-222-1-1-1-122-1-1-1-11100-2-21111-2-2-1-1-200011000002000-1-1110000000
χ3122222-1222-122-1-1222-1-1-22-1-1-12-1-1-1211-2-21111-2-222-1-1-1-1-1-1-1-1-2-2-2111111-2002-2-21111-2-21111-1-10022-1-1-1-1-2-2112000-1-1000002000-1-1110000000
χ3222222-1222-122-1-1222-1-1-22-1-1-12-1-1-1211-2-21111-2-2-2-21111-1-1-1-1-2-2-211111120022211-1-1-2-2-1-1-1-1-1-100-2-2111122112000-1-100000-200011-1-10000000
χ332222-122-1222-1222-1-1-122-1-1-12-122-1-122-1-1-1-1-1-100222222-1-1-1-12-1-122-1-1-1-12220-1-1002200-1-1-1-10022-1-1-1-1-1-100000-1-1200-1-1-1-1000220000000-1-100
χ342222-122-1222-1222-1-1-122-1-1-12-122-1-122-1-1-1-1-1-100222222-1-1-1-12-1-122-1-1-1-12-2-20-1-1002200-1-1-1-100-2-2-1-1-1-1-1-10000011-2001111000-2-200000001100
χ352222-122-1222-1222-1-1-122-1-1-12-122-1-122-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-1-22201100-2-2001111002211111100000-1-1200-1-1-1-1000-2-200000001100
χ362222-122-1222-1222-1-1-122-1-1-12-122-1-122-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-1-2-2-201100-2-200111100-2-21111110000011-2001111000220000000-1-100
χ372222-122-1222-1222-1-1-12-2-1-1-12-122-1-1-2-211111100222222-1-1-1-1-211-2-21111-22-201100-2-20011110022-1-1-1-1-1-100000-11-200-1-1110002-20000000-1100
χ382222-122-1222-1222-1-1-12-2-1-1-12-122-1-1-2-211111100222222-1-1-1-1-211-2-21111-2-2201100-2-200111100-2-2-1-1-1-1-1-1000001-120011-1-1000-2200000001-100
χ392222-122-1222-1222-1-1-12-2-1-1-12-122-1-1-2-211111100-2-2-2-2-2-2-1-1-1-1-211-2-2111122-20-1-1002200-1-1-1-1002211111100000-11-200-1-111000-2200000001-100
χ402222-122-1222-1222-1-1-12-2-1-1-12-122-1-1-2-211111100-2-2-2-2-2-2-1-1-1-1-211-2-211112-220-1-1002200-1-1-1-100-2-2111111000001-120011-1-10002-20000000-1100
χ4122-2-2222-2-2-2-222-22-22220-22-22-2-2-2-22000000002-22i−2i2i2i−2i−2i22-2-20000000000000002-2002-2000000002i−2i2i2i−2i−2i2i−2i2-2000000000000000002i−2i0000000
χ4222-2-2222-2-2-2-222-22-22220-22-22-2-2-2-22000000002-2−2i2i−2i−2i2i2i22-2-20000000000000002-2002-200000000−2i2i−2i−2i2i2i−2i2i2-200000000000000000−2i2i0000000
χ4322-2-2222-2-2-2-222-22-22220-22-22-2-2-2-2200000000-222i−2i2i2i−2i−2i22-2-2000000000000000-2200-22000000002i−2i2i2i−2i−2i−2i2i-2200000000000000000−2i2i0000000
χ4422-2-2222-2-2-2-222-22-22220-22-22-2-2-2-2200000000-22−2i2i−2i−2i2i2i22-2-2000000000000000-2200-2200000000−2i2i−2i−2i2i2i2i−2i-22000000000000000002i−2i0000000
χ4522-2-22-12-2-21-22-112-22-1-10-2-11-1-211123−30033−3−32-22i−2i−i−iii-1-1110003−333−3−3000000-11−i3i32-2−i3−i3i3i33−3002i−2i−i−iii2i−2i-1100003−3000000000−i3i3−ii0000000
χ4622-2-22-12-2-21-22-112-22-1-10-2-11-1-211123−30033−3−32-2−2i2iii−i−i-1-1110003−333−3−3000000-11i3−i32-2i3i3−i3−i33−300−2i2iii−i−i−2i2i-1100003−3000000000i3−i3i−i0000000
χ4722-2-22-12-2-21-22-112-22-1-10-2-11-1-211123−30033−3−3-222i−2i−i−iii-1-1110003−333−3−30000001-1−i3i3-22−i3−i3i3i3−33002i−2i−i−iii−2i2i1-10000−33000000000i3−i3i−i0000000
χ4822-2-22-12-2-21-22-112-22-1-10-2-11-1-211123−30033−3−3-22−2i2iii−i−i-1-1110003−333−3−30000001-1i3−i3-22i3i3−i3−i3−3300−2i2iii−i−i2i−2i1-10000−33000000000−i3i3−ii0000000
χ4922-2-22-12-2-21-22-112-22-1-10-2-11-1-21112−3300−3−3332-22i−2i−i−iii-1-111000−33−3−333000000-11i3−i32-2i3i3−i3−i3−33002i−2i−i−iii2i−2i-110000−33000000000i3−i3−ii0000000
χ5022-2-22-12-2-21-22-112-22-1-10-2-11-1-21112−3300−3−3332-2−2i2iii−i−i-1-111000−33−3−333000000-11−i3i32-2−i3−i3i3i3−3300−2i2iii−i−i−2i2i-110000−33000000000−i3i3i−i0000000
χ5122-2-22-12-2-21-22-112-22-1-10-2-11-1-21112−3300−3−333-222i−2i−i−iii-1-111000−33−3−3330000001-1i3−i3-22i3i3−i3−i33−3002i−2i−i−iii−2i2i1-100003−3000000000−i3i3i−i0000000
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χ5344444-2-24-2-2-24-2-2-24-2-214-2-2-21-211-2-2-2-244-2-2-2-2440000001111-2-2-2111111000400-2-200-2-20000-2-2000000000011-20001100000000000000000000
χ5444444-2-24-2-2-24-2-2-24-2-214-2-2-21-211-2-2-2-244-2-2-2-2-4-40000001111-2-2-2111111000-4002200220000220000000000-1-12000-1-100000000000000000000
χ5544444-2-24-2-2-24-2-2-24-2-21-4-2-2-21-211-2-222-4-42222440000001111222-1-1-1-1-1-1000-400-2-200-2-20000220000000000112000-1-100000000000000000000
χ5644444-2-24-2-2-24-2-2-24-2-21-4-2-2-21-211-2-222-4-42222-4-40000001111222-1-1-1-1-1-10004002200220000-2-20000000000-1-1-20001100000000000000000000
χ574444-24-2-2-24-2-244-2-21-2-241-2-2-21-2-2-2144-2-2-2-2-2-2000000001111-211-2-21111044000000000000000-2-200000000000-2-2-20011110000000000000000
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χ594444-24-2-2-24-2-244-2-21-2-2-41-2-2-21-2-2-21-4-42222220000000011112-1-122-1-1-1-104-4000000000000000-2-200000000000-2220011-1-10000000000000000
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χ7044-4-44-2-2-42224-22-2-4-2-2102-2212-1-12-2−232300−23−232323-4400000011-1-10003−333−3−30000002-2002-2000023−230000000000-110000−3300000000000000000000
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χ7544-4-4-2-242-42-4-2-2242-21-2021-1-2222-1-2−23230033−3−3004i−4i−2i−2i2i2i11-1-1000−232333−3−3000000002i3−2i300−i3−i3i3i30000−2i2iii−i−i000000000000000000000000000000
χ7644-4-4-2-242-42-4-2-2242-21-2021-1-2222-1-2−23230033−3−300−4i4i2i2i−2i−2i11-1-1000−232333−3−300000000−2i32i300i3i3−i3−i300002i−2i−i−iii000000000000000000000000000000
χ774-44-44444-444-4-4-4-4-444404-44-4-4-44-4-400000000000000004-44-400000000000000000000000000000000000000000000000000000000000000000
χ784-44-444-2424-2-4-4-42-4-24-20-2-44222-2-420000000000000000-22-22000000000000000000000000000000000000000000000000000000000023−2300000
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χ854-44-4-2-24-2-4-24222-42-21-20-2-11222-2-1200003i−3i3i−3i0000−2323−23231-11-1000003i−3i3i−3i00002i3−2i3000000−i3i3−i3i30000003−33−3000000000000000000000000000000
χ864-44-4-2-24-2-4-24222-42-21-20-2-11222-2-120000−3i3i−3i3i000023−2323−231-11-100000−3i3i−3i3i00002i3−2i3000000−i3i3−i3i3000000−33−33000000000000000000000000000000
χ874-44-4-2-24-2-4-24222-42-21-20-2-11222-2-120000−3i3i−3i3i0000−2323−23231-11-100000−3i3i−3i3i0000−2i32i3000000i3−i3i3−i30000003−33−3000000000000000000000000000000
χ884-4-44444-44-4-4-4-44-444440-4-4-4-444-44-400000000000000004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ894-4-4444-2-4-2-42-4-4424-24-202-4-42-2-22420000000000000000-222-200000000000000000000000000023−23000000000000000023−23000000000000000000
χ904-4-4444-2-4-2-42-4-4424-24-202-4-42-2-22420000000000000000-222-2000000000000000000000000000−23230000000000000000−2323000000000000000000
χ914-4-444-24-442-4-42-2-444-2-20-42224-22-2-4000000000000−2i32i32i3−2i3-222-20000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ924-4-444-24-442-4-42-2-444-2-20-42224-22-2-40000000000002i3−2i3−2i32i3-222-200000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000000000
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χ944-4-44-24424-4-42-44-4-2-2-240222-4-24-4-22002i3−2i32i3−2i3−2i32i300000000-222-202i3−2i3002i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ954-4-44-24-22-2-422-442-21-2-20-12221-22-2-100−2i32i3−2i32i32i3−2i3000000001-1-110i3−i300i3−i3−i3i300000000000000000023−230000000000000000−333i−3i0000000000000000
χ964-4-44-24-22-2-422-442-21-2-20-12221-22-2-100−2i32i3−2i32i32i3−2i3000000001-1-110i3−i300i3−i3−i3i3000000000000000000−232300000000000000003−3−3i3i0000000000000000
χ974-4-44-24-22-2-422-442-21-2-20-12221-22-2-1002i3−2i32i3−2i3−2i32i3000000001-1-110−i3i300−i3i3i3−i300000000000000000023−230000000000000000−33−3i3i0000000000000000
χ984-4-44-24-22-2-422-442-21-2-20-12221-22-2-1002i3−2i32i3−2i3−2i32i3000000001-1-110−i3i300−i3i3i3−i3000000000000000000−232300000000000000003−33i−3i0000000000000000
χ994-4-44-2-24242-422-2-4-2-21-202-1-12-2-221200−2i32i3i3−i3−i3i30000−2i32i32i3−2i31-1-110−2i32i300i3−i3−i3i30000000000003-3-33000000i3−i3−i3i3000000000000000000000000000000
χ1004-4-44-2-24242-422-2-4-2-21-202-1-12-2-221200−2i32i3i3−i3−i3i300002i3−2i3−2i32i31-1-110−2i32i300i3−i3−i3i3000000000000-333-3000000−i3i3i3−i3000000000000000000000000000000
χ1014-4-44-2-24242-422-2-4-2-21-202-1-12-2-2212002i3−2i3−i3i3i3−i30000−2i32i32i3−2i31-1-1102i3−2i300−i3i3i3−i3000000000000-333-3000000i3−i3−i3i3000000000000000000000000000000
χ1024-4-44-2-24242-422-2-4-2-21-202-1-12-2-2212002i3−2i3−i3i3i3−i300002i3−2i3−2i32i31-1-1102i3−2i300−i3i3i3−i30000000000003-3-33000000−i3i3i3−i3000000000000000000000000000000
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
χ10588-8-8-48-444-84-48-8-442-4-40-2-44-4-24442000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-44444-4-44-442220-22-22-2-2-2-2243−4300−23−23232300000000-1-111000−232333−3−300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-44444-4-44-442220-22-22-2-2-2-22−4343002323−23−2300000000-1-11100023−23−3−33300000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-484-4-4-8444-8-4-420-44-4-24-224400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-48-4-448-44-8-8442-4-4024-44-24-44-200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4-44-4-44444422202-22-2-2-22-2-200006i−6i6i−6i00000000-11-1100000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-4-44-4-44444422202-22-2-2-22-2-20000−6i6i−6i6i00000000-11-11000003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1128-8-888-4-4-8-444-84-448-4-420444-2-42-2-4400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-44-44444-44-42220-2-2-2-222-22-200−4i34i32i3−2i3−2i32i300000000-111-102i3−2i300−i3i3i3−i300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-44-44444-44-42220-2-2-2-222-22-2004i3−4i3−2i32i32i3−2i300000000-111-10−2i32i300i3−i3−i3i300000000000000000000000000000000000000000000000000000000

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