Finite Group Databasebeta

← Group #13172369

Character table — Group #13172369

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size111122222222222244444444444444488888888888888881212121212121212121212121212242424242424242424242424242424242424242436363636363636363636363636367272108108
order1222333666666666233366666666666366666666666666622444466661212121266666612121212121212121212121212124444441212121212121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-111-1111111-1-1111111-1-1-11111111-1-1-1-11-1-1-11-111-1-1-1-1-1-1-11-1-1
χ3111111111111111111111111111111111111111111111111-111-11-1-111-1-1111-111-1-11111-1111-1-11111-111-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-11-1-1-1-111-1-1-1-11-111-1-1-1-1-11-1111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11-111
χ511111111111111111111111111111111111111111111111-111-11111-1-11111-11-1-111111-11-1-1-1111111-1-1-11-11-1-111-1-1-1-11-1-1-1
χ611111111111111111111111111111111111111111111111-11-1-11-111-1-111-1-1-11-1-111-1-1-1-11-1-1-111-1-1-1-1-111-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111111111111111111111111-1-11-1-11-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1-11-111-1-1-1-1-1-1-1111
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-11-1-1-1-1-1-111-1-111-11
χ101111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-111111-1-111111111-1-11-1-1-1-1-1-1-1-1-1111-11-1-11-1-111-1-111-111-1
χ111111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-11-11-1-1-11111-1-11-111-1-111-1-11-1-1-11111-1-1-11-1-111111111-1-1-1-11-1
χ121111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-111-1-11111111-111-1-1-1-11-11-1-1-111-1-111-1-1111-111-1-1-1-1111-1-11
χ131111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-111-1-1-1-1-1-1-11-1-11111-11-1111-1-111-1-1-1-1111-111-1-1-1-1111-11-1
χ141111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-1111-1-1-1-111-11-1-111-1-111-1111-1-1-1-111-11-1-111111111-1-1-1-1-11
χ151111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-1-1-1-111-1111111111-1-11-11-1-11-1-111-1-111-11-11
χ161111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-11-1-1-1-1-1-111-1-1111-1
χ17222222-1-12222-1-12222-1-1222-1-1-1-122-1-1-12-122-1-1-1-1-1-1-1-1-1-1-122022022-1-1-1-1002-1-1-1-1-1000-122-1-1-1-10000200020-1-10000000-100
χ18222222-1-12222-1-12222-1-1222-1-1-1-122-1-1-12-122-1-1-1-1-1-1-1-1-1-1-12-202-20-2-2-1-1110021-1-111000-1-22-1-1110000-2000-20110000000100
χ19222222-1-12222-1-12222-1-1222-1-1-1-122-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1-220-2202211-1-100-2-111-1-100012-211-1-10000-2000-20110000000100
χ20222222-1-12222-1-12222-1-1222-1-1-1-122-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1-2-20-2-20-2-2111100-2111110001-2-211110000200020-1-10000000-100
χ21222222-1-12222-1-122-22-1-1-2-22-1-1-1-122-1-1-1-21-2-21111-1-1-11111220-2-2022-1-111002-1-1-1-1-10001-2-2111100002000-20110000000-100
χ22222222-1-12222-1-122-22-1-1-2-22-1-1-1-122-1-1-1-21-2-21111-1-1-111112-20-220-2-2-1-1-1-10021-1-11100012-211-1-10000-200020-1-10000000100
χ23222222-1-12222-1-122-22-1-1-2-22-1-1-1-122-1-1-1-21-2-21111-1-1-11111-2202-2022111100-2-111-1-1000-1-22-1-1110000-200020-1-10000000100
χ24222222-1-12222-1-122-22-1-1-2-22-1-1-1-122-1-1-1-21-2-21111-1-1-11111-2-20220-2-211-1-100-211111000-122-1-1-1-100002000-20110000000-100
χ2522222-12222-1-122-122-12-122-122-1-1-1-12-1-1-12-1-122-1-1-1-1-1-1-1-1-1022022-1-10022-1-10200-1-12-120-1000-1-1-1-1-1-100020200-1-10000-1000
χ2622222-12222-1-122-122-12-122-122-1-1-1-12-1-1-12-1-122-1-1-1-1-1-1-1-1-102-202-2-1-10022110200-1-1-21-20-1000-1-11111000-20-2001100001000
χ2722222-12222-1-122-122-12-122-122-1-1-1-12-1-1-12-1-122-1-1-1-1-1-1-1-1-10-220-221100-2-2-1-10-200112-120100011-1-1-1-1000-20-2001100001000
χ2822222-12222-1-122-122-12-122-122-1-1-1-12-1-1-12-1-122-1-1-1-1-1-1-1-1-10-2-20-2-21100-2-2110-20011-21-20100011111100020200-1-10000-1000
χ2922222-12222-1-122-12-2-12-1-2-2-122-1-1-1-12-1-11-211-2-211-1-1-111110220-2-2-1-100-2-2110200-1-12-1-20100011-1-11100020-200110000-1000
χ3022222-12222-1-122-12-2-12-1-2-2-122-1-1-1-12-1-11-211-2-211-1-1-1111102-20-22-1-100-2-2-1-10200-1-1-212010001111-1-1000-20200-1-100001000
χ3122222-12222-1-122-12-2-12-1-2-2-122-1-1-1-12-1-11-211-2-211-1-1-111110-2202-2110022110-200112-1-20-1000-1-1-1-111000-20200-1-100001000
χ3222222-12222-1-122-12-2-12-1-2-2-122-1-1-1-12-1-11-211-2-211-1-1-111110-2-2022110022-1-10-20011-2120-1000-1-111-1-100020-200110000-1000
χ332222-1222-1-122222-12-1-12-1-1-1-1-122-1-1-12-122-1-1-1-122-1-1-1-1-1-1-120220200220022-10-1-100-12-120-1-1-100-1-1-1-10220000000-1-1-1-10000
χ342222-1222-1-122222-12-1-12-1-1-1-1-122-1-1-12-122-1-1-1-122-1-1-1-1-1-1-120-220-2002200-2-2-10-1-1001-2120-1-1-10011110-2-2000000011110000
χ352222-1222-1-122222-12-1-12-1-1-1-1-122-1-1-12-122-1-1-1-122-1-1-1-1-1-1-1-202-20200-2-20022101100-12-1-2011100-1-1-1-10-2-2000000011110000
χ362222-1222-1-122222-12-1-12-1-1-1-1-122-1-1-12-122-1-1-1-122-1-1-1-1-1-1-1-20-2-20-200-2-200-2-21011001-21-201110011110220000000-1-1-1-10000
χ372222-1222-1-122222-1-2-1-1211-1-1-122-1-1-12-1-2-21111-2-2-1-1-11111202-20-2002200-2-2-10-1-100-121-2011100-1-11102-20000000-1-1110000
χ382222-1222-1-122222-1-2-1-1211-1-1-122-1-1-12-1-2-21111-2-2-1-1-1111120-2-20200220022-10-1-1001-2-1-201110011-1-10-22000000011-1-10000
χ392222-1222-1-122222-1-2-1-1211-1-1-122-1-1-12-1-2-21111-2-2-1-1-11111-20220-200-2-200-2-2101100-12120-1-1-100-1-1110-22000000011-1-10000
χ402222-1222-1-122222-1-2-1-1211-1-1-122-1-1-12-1-2-21111-2-2-1-1-11111-20-220200-2-200221011001-2-120-1-1-10011-1-102-20000000-1-1110000
χ4144444-2-2-244-2-2-2-2-244-2-2144-2-2-211-2-2-211-2-2-2-2-2-2111111111040040-2-200-2-2000-200110000-2000110000000000000000000000
χ4244444-2-2-244-2-2-2-2-244-2-2144-2-2-211-2-2-211-2-2-2-2-2-21111111110-400-40220022000200-1-100002000-1-10000000000000000000000
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χ4444444-2-2-244-2-2-2-2-24-4-2-21-4-4-2-2-211-2-2-211222222-1-1111-1-1-1-10-400402200-2-2000200-1-10000-2000110000000000000000000000
χ454444-24-2-2-2-244-2-24-24-21-2-2-2-211-2-2-2-21-214-2-2-211-2-2111111140040000-2-20000-201100000-20-211000000000000000000000000
χ464444-24-2-2-2-244-2-24-24-21-2-2-2-211-2-2-2-21-214-2-2-211-2-21111111-400-4000022000020-1-100000202-1-1000000000000000000000000
χ474444-24-2-2-2-244-2-24-2-4-21-222-211-2-2-2-21-21-4222-1-122111-1-1-1-1400-40000-2-20000-201100000202-1-1000000000000000000000000
χ484444-24-2-2-2-244-2-24-2-4-21-222-211-2-2-2-21-21-4222-1-122111-1-1-1-1-4004000022000020-1-100000-20-211000000000000000000000000
χ494444-2-244-2-2-2-244-2-241-2-2-2-21-2-2-2-211-2-21-2411-2-2-2-21111111004004000000-2-2000000-2-2-200000001111000000000000000000
χ504444-2-244-2-2-2-244-2-241-2-2-2-21-2-2-2-211-2-21-2411-2-2-2-2111111100-400-4000000220000002220000000-1-1-1-1000000000000000000
χ514444-2-244-2-2-2-244-2-2-41-2-2221-2-2-2-211-2-212-4-1-12222111-1-1-1-100400-400000022000000-2-22000000011-1-1000000000000000000
χ524444-2-244-2-2-2-244-2-2-41-2-2221-2-2-2-211-2-212-4-1-12222111-1-1-1-100-4004000000-2-200000022-20000000-1-111000000000000000000
χ5344-4-444444-44-4-4-4-4-4044400-44-44-44-4-4-44000000004-4-400000000000000000000000000000000000000000000000000000000
χ5444-4-444-2-24-44-422-4-404-2-200-4-22-224-422-200000000-2220000000000000000000000000000000000000000000023−230000000000
χ5544-4-444-2-24-44-422-4-404-2-200-4-22-224-422-200000000-22200000000000000000000000000000000000000000000−23230000000000
χ5644-4-44-2444-4-22-4-42-40-24-20024-4-22-22-42-200000000-222000000000000000000000000000000000000000000000023−2300000000
χ5744-4-44-2444-4-22-4-42-40-24-20024-4-22-22-42-200000000-2220000000000000000000000000000000000000000000000−232300000000
χ5844-4-4-2444-224-4-4-4-420-2-24002-224-4-222-4-200000000-2220000000000000000000000000000000000000000000000000023−230000
χ5944-4-4-2444-224-4-4-4-420-2-24002-224-4-222-4-200000000-22200000000000000000000000000000000000000000000000000−23230000
χ604-44-4444-4-4-4-444-4-440444004-4-4-44-4-44-4400000000-44-400000000000000000000000000000000000000000000000000000000
χ614-44-444-22-4-4-44-22-4404-2-2004222-2-4-4-22-2000000002-22000000000000−2i32i3000000−2i32i30000000000000000000000000000000000
χ624-44-444-22-4-4-44-22-4404-2-2004222-2-4-4-22-2000000002-220000000000002i3−2i30000002i3−2i30000000000000000000000000000000000
χ634-44-44-24-4-4-42-24-4240-24-200-2-4-42-22242-2000000002-22000000000000000023−2300000000000000000023−23000000000000000000
χ644-44-44-24-4-4-42-24-4240-24-200-2-4-42-22242-2000000002-220000000000000000−2323000000000000000000−2323000000000000000000
χ654-44-4-244-422-444-4-4-20-2-24−2i32i3-222-4422-2-4-200−2i32i3−2i32i3002-22−2i3−2i32i32i30000000000000000000000000000000000000000000000000000
χ664-44-4-244-422-444-4-4-20-2-242i3−2i3-222-4422-2-4-2002i3−2i32i3−2i3002-222i32i3−2i3−2i30000000000000000000000000000000000000000000000000000
χ674-44-4-24-2222-44-22-4-20-21-2−2i32i3-2-1-12-22212100−2i32i3i3−i300-11-1i3i3−i3−i300000000−2i32i3000000i3−i3000000003-3000000000000000000000000
χ684-44-4-24-2222-44-22-4-20-21-2−2i32i3-2-1-12-22212100−2i32i3i3−i300-11-1i3i3−i3−i3000000002i3−2i3000000−i3i300000000-33000000000000000000000000
χ694-44-4-24-2222-44-22-4-20-21-22i3−2i3-2-1-12-222121002i3−2i3−i3i300-11-1−i3−i3i3i300000000−2i32i3000000i3−i300000000-33000000000000000000000000
χ704-44-4-24-2222-44-22-4-20-21-22i3−2i3-2-1-12-222121002i3−2i3−i3i300-11-1−i3−i3i3i3000000002i3−2i3000000−i3i3000000003-3000000000000000000000000
χ714-44-4-2-24-4222-24-42-201-2-2−2i32i31222-2-1-1-22100i3−i3−2i32i300-11-1i3i3−i3−i300000000000023−2300000000000000003i−3i−33000000000000000000
χ724-44-4-2-24-4222-24-42-201-2-2−2i32i31222-2-1-1-22100i3−i3−2i32i300-11-1i3i3−i3−i3000000000000−23230000000000000000−3i3i3−3000000000000000000
χ734-44-4-2-24-4222-24-42-201-2-22i3−2i31222-2-1-1-22100−i3i32i3−2i300-11-1−i3−i3i3i300000000000023−230000000000000000−3i3i−33000000000000000000
χ744-44-4-2-24-4222-24-42-201-2-22i3−2i31222-2-1-1-22100−i3i32i3−2i300-11-1−i3−i3i3i3000000000000−232300000000000000003i−3i3−3000000000000000000
χ754-4-44444-4-44-4-4-444-4044400-4-44-4-4-44-44400000000-4-4400000000000000000000000000000000000000000000000000000000
χ764-4-4444-22-44-4-42-24-404-2-200-42-222-442-2-20000000022-200000000000000−2i32i30000000000000000−2i32i30000000000000000000000
χ774-4-4444-22-44-4-42-24-404-2-200-42-222-442-2-20000000022-2000000000000002i3−2i300000000000000002i3−2i30000000000000000000000
χ784-4-444-24-4-4422-44-2-40-24-2002-44222-2-4-2-20000000022-20000000000−2i32i30000000000−2i32i300000000000000000000000000000000
χ794-4-444-24-4-4422-44-2-40-24-2002-44222-2-4-2-20000000022-200000000002i3−2i300000000002i3−2i300000000000000000000000000000000
χ804-4-444-2-22-44222-2-2-40-2-210022-2-1-12-22110000003-3-1-113-33-3000000−2i32i300−2i32i3000000i3−i300000000i3−i30000000000000000000000
χ814-4-444-2-22-44222-2-2-40-2-210022-2-1-12-22110000003-3-1-113-33-30000002i3−2i3002i3−2i3000000−i3i300000000−i3i30000000000000000000000
χ824-4-444-2-22-44222-2-2-40-2-210022-2-1-12-2211000000-33-1-11-33-33000000−2i32i3002i3−2i3000000i3−i300000000−i3i30000000000000000000000
χ834-4-444-2-22-44222-2-2-40-2-210022-2-1-12-2211000000-33-1-11-33-330000002i3−2i300−2i32i3000000−i3i300000000i3−i30000000000000000000000
χ844-4-44-244-42-2-4-4-44420-2-240022-2-4-42-224-20000000022-200000000000000000000000000000000000000000000000023−23000000
χ854-4-44-244-42-2-4-4-44420-2-240022-2-4-42-224-20000000022-2000000000000000000000000000000000000000000000000−2323000000
χ868888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4222222222-1-4-4222222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000
χ878888-4-4-4-4-4-4-4-4-4-4-4-4-822244222222222-144-2-2-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000
χ8888-8-88-4-4-48-8-44444-80-4-42004-442-2-444-22000000002-2-200000000000000000000000000000000000000000000000000000000
χ8988-8-8-48-4-4-448-844-840-42-40042-2-44-44-242000000002-2-200000000000000000000000000000000000000000000000000000000
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χ9188-8-8-4-4-4-4-44-444444022200-22-22-22-2-2-2-100000000-111−3i33i33i3−3i30000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-4-4-44-444444022200-22-22-22-2-2-2-100000000-1113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000
χ938-88-88-4-44-8-84-4-44480-4-4200-444-2244-4-2200000000-22-200000000000000000000000000000000000000000000000000000000
χ948-88-8-4-4-44444-4-444-40222−4i34i32-2-2-22-2-22-2-1002i3−2i32i3−2i3001-11−i3−i3i3i30000000000000000000000000000000000000000000000000000
χ958-88-8-4-4-44444-4-444-402224i3−4i32-2-2-22-2-22-2-100−2i32i3−2i32i3001-11i3i3−i3−i30000000000000000000000000000000000000000000000000000
χ968-8-88-48-444-4-8-84-4840-42-4004-22444-4-2-4200000000-2-2200000000000000000000000000000000000000000000000000000000
χ978-8-88-4-48-84-444-88-4402-4-400-24-444-224-4200000000-2-2200000000000000000000000000000000000000000000000000000000
χ988-8-88-4-4-444-4444-4-44022200-2-22-2-2-22-22-10000006-611-1-33-330000000000000000000000000000000000000000000000000000
χ998-8-88-4-4-444-4444-4-44022200-2-22-2-2-22-22-1000000-6611-13-33-30000000000000000000000000000000000000000000000000000

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