Finite Group Databasebeta

← Group #10692278

Character table — Group #10692278

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222224444444444444444444444444444444444448888888888888888888888888824242424484848484848
order12223444444666121212122224444466668888121212121212121212121212242424242424242444688888812121212122424242424242424242424248888448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ4111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111111111111-1-111-1-11-1-1-1-1111111111111-1-1-1-111111111-1-1111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ61111111111111111111-1-111-1-11-1-1-1-1111111111111-1-1-1-111111111-1-1111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ71111111111111111111-1-111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ81111111111111111111-1-111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ9111111-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−i1111-1-1-1-1-1-1-1-1iiii−i−i−i−i1-11i−iii−i−i-111-1-1ii−i−iiiii−i−i−i−iii−i−i1-1i−i1-1
χ10111111-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−i1111-1-1-1-1-1-1-1-1iiii−i−i−i−i1-11i−iii−i−i-111-1-1ii−i−iiiii−i−i−i−i−i−iii-11−ii-11
χ11111111-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iii1111-1-1-1-1-1-1-1-1−i−i−i−iiiii1-11−ii−i−iii-111-1-1−i−iii−i−i−i−iiiiiii−i−i-11i−i-11
χ12111111-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iii1111-1-1-1-1-1-1-1-1−i−i−i−iiiii1-11−ii−i−iii-111-1-1−i−iii−i−i−i−iiiii−i−iii1-1−ii1-1
χ13111111-1-1-1-11111-1-1-1-11-1-11-111-1-1-1-1-1ii−i−i1111-1-1-1-11111iiii−i−i−i−i-111i−i−i−iii-1-1-111ii−i−i−i−i−i−iiiiiii−i−i-11−ii1-1
χ14111111-1-1-1-11111-1-1-1-11-1-11-111-1-1-1-1-1ii−i−i1111-1-1-1-11111iiii−i−i−i−i-111i−i−i−iii-1-1-111ii−i−i−i−i−i−iiiii−i−iii1-1i−i-11
χ15111111-1-1-1-11111-1-1-1-11-1-11-111-1-1-1-1-1−i−iii1111-1-1-1-11111−i−i−i−iiiii-111−iiii−i−i-1-1-111−i−iiiiiii−i−i−i−iii−i−i1-1−ii-11
χ16111111-1-1-1-11111-1-1-1-11-1-11-111-1-1-1-1-1−i−iii1111-1-1-1-11111−i−i−i−iiiii-111−iiii−i−i-1-1-111−i−iiiiiii−i−i−i−i−i−iii-11i−i1-1
χ1722222222-2-222222222-222-2222-22222000022-2-222-2-2222200000000-2-2-2000000-2-2-2-2-20000000000000000000000
χ1822222222-2-222222222-2-2-2-22-2-2-2-2-2-2-2000022-2-222-2-2-2-2-2-20000000022-2000000-222220000000000000000000000
χ19222222-2-2222222-2-2-2-2-222-2-2-2-222222000022-2-2-2-222-2-2-2-200000000-22-20000002-2-2220000000000000000000000
χ20222222-2-2222222-2-2-2-2-2-2-2-2-2222-2-2-2-2000022-2-2-2-2222222000000002-2-2000000222-2-20000000000000000000000
χ2122222-22222-22222222-2002-200-200002222-2-222-2-22200002222222200-2-2-20000-20000-2-2-2-2000000000000000000
χ2222222-22222-22222222-2002-200-20000-2-2-2-2-2-222-2-2220000-2-2-2-2-2-2-2-200-2220000-200002222000000000000000000
χ2322222-222-2-2-22222222200-2-200200000000-2-2-2-2-2-2-2-2000000000000002002-22-220000000022-2-222-2-20000000000
χ2422222-222-2-2-22222222200-2-200200000000-2-2-2-2-2-2-2-200000000000000200-22-22200000000-2-222-2-2220000000000
χ2522222-2-2-222-2222-2-2-2-2200-2200-200000000-2-2-2-22222000000000000002002i−2i−2i2i-2000000002i2i−2i−2i−2i−2i2i2i0000000000
χ2622222-2-2-222-2222-2-2-2-2200-2200-200000000-2-2-2-2222200000000000000200−2i2i2i−2i-200000000−2i−2i2i2i2i2i−2i−2i0000000000
χ2722222-2-2-2-2-2-2222-2-2-2-2-2002200200002i2i−2i−2i-2-22222-2-200002i2i2i2i−2i−2i−2i−2i00-2−2i2i000020000−2i−2i2i2i000000000000000000
χ2822222-2-2-2-2-2-2222-2-2-2-2-200220020000−2i−2i2i2i-2-22222-2-20000−2i−2i−2i−2i2i2i2i2i00-22i−2i0000200002i2i−2i−2i000000000000000000
χ292222-1222222-1-1-1-1-1-1-122222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ302222-1222222-1-1-1-1-1-1-122222222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111122-1-2-2-2-2-2-2-1-1-1-1-11111111111110000000000
χ312222-1222222-1-1-1-1-1-1-12-2-222-2-2211112222-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-2-122-2-2-2-2-11111-1-1-1-1111111110000000000
χ322222-1222222-1-1-1-1-1-1-12-2-222-2-221111-2-2-2-2-1-1-1-1-1-1-1-1111111111111-2-2-1-2-22222-111111111-1-1-1-1-1-1-1-10000000000
χ332222-1222-2-22-1-1-1-1-1-1-1-222-2222-2-1-1-1-10000-1-111-1-111-1-1-1-1−i3−i3i3i3−i3−i3i3i3-2-2100000011111−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000000000
χ342222-1222-2-22-1-1-1-1-1-1-1-222-2222-2-1-1-1-10000-1-111-1-111-1-1-1-1i3i3−i3−i3i3i3−i3−i3-2-2100000011111i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000000000
χ352222-1222-2-22-1-1-1-1-1-1-1-2-2-2-22-2-2-211110000-1-111-1-1111111−i3−i3i3i3−i3−i3i3i32210000001-1-1-1-1−i3i3−i3i3i3−i3i3−i3i3−i3i3−i30000000000
χ362222-1222-2-22-1-1-1-1-1-1-1-2-2-2-22-2-2-211110000-1-111-1-1111111i3i3−i3−i3i3i3−i3−i32210000001-1-1-1-1i3−i3i3−i3−i3i3−i3i3−i3i3−i3i30000000000
χ372222-12-2-2222-1-1-11111-222-2-2-2-22-1-1-1-10000-1-11111-1-1111133−3−3−3−333-221000000-111-1-13−3−333−33−3−33−330000000000
χ382222-12-2-2222-1-1-11111-222-2-2-2-22-1-1-1-10000-1-11111-1-11111−3−33333−3−3-221000000-111-1-1−333−3−33−333−33−30000000000
χ392222-12-2-2222-1-1-11111-2-2-2-2-222211110000-1-11111-1-1-1-1-1-133−3−3−3−3332-21000000-1-1-1113−3−33−33−333−33−30000000000
χ402222-12-2-2222-1-1-11111-2-2-2-2-222211110000-1-11111-1-1-1-1-1-1−3−33333−3−32-21000000-1-1-111−333−33−33−3−33−330000000000
χ412222-12-2-2-2-22-1-1-111112222-2-2-2-2-1-1-1-12i2i−2i−2i-1-1-1-111111111−i−i−i−iiiii2-2-12i−2i2i2i−2i−2i1-1-111−i−iii−i−i−i−iiiii0000000000
χ422222-12-2-2-2-22-1-1-111112222-2-2-2-2-1-1-1-1−2i−2i2i2i-1-1-1-111111111iiii−i−i−i−i2-2-1−2i2i−2i−2i2i2i1-1-111ii−i−iiiii−i−i−i−i0000000000
χ432222-12-2-2-2-22-1-1-111112-2-22-222-211112i2i−2i−2i-1-1-1-11111-1-1-1-1−i−i−i−iiiii-22-12i−2i−2i−2i2i2i111-1-1−i−iiiiiii−i−i−i−i0000000000
χ442222-12-2-2-2-22-1-1-111112-2-22-222-21111−2i−2i2i2i-1-1-1-11111-1-1-1-1iiii−i−i−i−i-22-1−2i2i2i2i−2i−2i111-1-1ii−i−i−i−i−i−iiiii0000000000
χ452222-1-22222-2-1-1-1-1-1-1-1-2002-200-2−i3−i3i3i3222211-1-111-1-1−i3−i3i3i3-1-1-1-1-1-1-1-1001-2-200001−i3i3−i3i31111−i3i3i3−i3−i3i3i3−i30000000000
χ462222-1-22222-2-1-1-1-1-1-1-1-2002-200-2−i3−i3i3i3-2-2-2-211-1-111-1-1−i3−i3i3i3111111110012200001−i3i3−i3i3-1-1-1-1i3−i3−i3i3i3−i3−i3i30000000000
χ472222-1-22222-2-1-1-1-1-1-1-1-2002-200-2i3i3−i3−i3222211-1-111-1-1i3i3−i3−i3-1-1-1-1-1-1-1-1001-2-200001i3−i3i3−i31111i3−i3−i3i3i3−i3−i3i30000000000
χ482222-1-22222-2-1-1-1-1-1-1-1-2002-200-2i3i3−i3−i3-2-2-2-211-1-111-1-1i3i3−i3−i3111111110012200001i3−i3i3−i3-1-1-1-1−i3i3i3−i3−i3i3i3−i30000000000
χ492222-1-222-2-2-2-1-1-1-1-1-1-1200-2-2002−i3−i3i3i3000011111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300-1002-22-2-1i3−i3i3−i3i3−i3i3−i3-1-111-1-1110000000000
χ502222-1-222-2-2-2-1-1-1-1-1-1-1200-2-2002−i3−i3i3i3000011111111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300-100-22-22-1i3−i3i3−i3−i3i3−i3i311-1-111-1-10000000000
χ512222-1-222-2-2-2-1-1-1-1-1-1-1200-2-2002i3i3−i3−i3000011111111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300-100-22-22-1−i3i3−i3i3i3−i3i3−i311-1-111-1-10000000000
χ522222-1-222-2-2-2-1-1-1-1-1-1-1200-2-2002i3i3−i3−i3000011111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300-1002-22-2-1−i3i3−i3i3−i3i3−i3i3-1-111-1-1110000000000
χ532222-1-2-2-222-2-1-1-11111200-2200-2−i3−i3i3i300001111-1-1-1-1i3i3−i3−i333−3−3−3−33300-1002i−2i−2i2i1i3−i3−i3i3−333−3−i−iiiii−i−i0000000000
χ542222-1-2-2-222-2-1-1-11111200-2200-2−i3−i3i3i300001111-1-1-1-1i3i3−i3−i3−3−33333−3−300-100−2i2i2i−2i1i3−i3−i3i33−3−33ii−i−i−i−iii0000000000
χ552222-1-2-2-222-2-1-1-11111200-2200-2i3i3−i3−i300001111-1-1-1-1−i3−i3i3i333−3−3−3−33300-100−2i2i2i−2i1−i3i3i3−i3−333−3ii−i−i−i−iii0000000000
χ562222-1-2-2-222-2-1-1-11111200-2200-2i3i3−i3−i300001111-1-1-1-1−i3−i3i3i3−3−33333−3−300-1002i−2i−2i2i1−i3i3i3−i33−3−33−i−iiiii−i−i0000000000
χ572222-1-2-2-2-2-2-2-1-1-11111-20022002−i3−i3i3i32i2i−2i−2i11-1-1-1-111i3i3−i3−i3−i−i−i−iiiii001−2i2i0000-1−i3i3i3−i3ii−i−i3−3−33−333−30000000000
χ582222-1-2-2-2-2-2-2-1-1-11111-20022002−i3−i3i3i3−2i−2i2i2i11-1-1-1-111i3i3−i3−i3iiii−i−i−i−i0012i−2i0000-1−i3i3i3−i3−i−iii−333−33−3−330000000000
χ592222-1-2-2-2-2-2-2-1-1-11111-20022002i3i3−i3−i32i2i−2i−2i11-1-1-1-111−i3−i3i3i3−i−i−i−iiiii001−2i2i0000-1i3−i3−i3i3ii−i−i−333−33−3−330000000000
χ602222-1-2-2-2-2-2-2-1-1-11111-20022002i3i3−i3−i3−2i−2i2i2i11-1-1-1-111−i3−i3i3i3iiii−i−i−i−i0012i−2i0000-1i3−i3−i3i3−i−iii3−3−33−333−30000000000
χ6144-4-4440000-44-4-4000004-4000004-44-400004-4000000000000000000000000000000000000000000000000000000
χ6244-4-4440000-44-4-400000-4400000-44-4400004-4000000000000000000000000000000000000000000000000000000
χ6344-4-44-4000044-4-40000000004i−4i000000000-440000004i−4i4i−4i00000000000000000000000000000000000000000000
χ6444-4-44-4000044-4-4000000000−4i4i000000000-44000000−4i4i−4i4i00000000000000000000000000000000000000000000
χ6544-4-4-240000-4-2222323−23−2304-400000-22-220000-220023−230023−23−232300000000000000000000000000000000000000000000
χ6644-4-4-240000-4-2222323−23−230-44000002-22-20000-220023−2300−232323−2300000000000000000000000000000000000000000000
χ6744-4-4-240000-4-222−23−23232304-400000-22-220000-2200−232300−232323−2300000000000000000000000000000000000000000000
χ6844-4-4-240000-4-222−23−2323230-44000002-22-20000-2200−23230023−23−232300000000000000000000000000000000000000000000
χ6944-4-4-2-400004-2222323−23−23000004i−4i0−2i32i32i3−2i300002-200−232300−2i2i−2i2i00000000000000000000000000000000000000000000
χ7044-4-4-2-400004-2222323−23−2300000−4i4i02i3−2i3−2i32i300002-200−2323002i−2i2i−2i00000000000000000000000000000000000000000000
χ7144-4-4-2-400004-222−23−232323000004i−4i02i3−2i3−2i32i300002-20023−2300−2i2i−2i2i00000000000000000000000000000000000000000000
χ7244-4-4-2-400004-222−23−23232300000−4i4i0−2i32i32i3−2i300002-20023−23002i−2i2i−2i00000000000000000000000000000000000000000000
χ734-44-440004i−4i0-44-400000000000000002+2i−2−2i2−2i−2+2i0000004i−4i00002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i000000000000000000000000000000000000
χ744-44-440004i−4i0-44-40000000000000000−2−2i2+2i−2+2i2−2i0000004i−4i0000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i000000000000000000000000000000000000
χ754-44-44000−4i4i0-44-400000000000000002−2i−2+2i2+2i−2−2i000000−4i4i00002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i000000000000000000000000000000000000
χ764-44-44000−4i4i0-44-40000000000000000−2+2i2−2i−2−2i2+2i000000−4i4i0000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i000000000000000000000000000000000000
χ774-44-4-20004i−4i02-22−2i32i3−2i32i30000000000002+2i−2−2i2−2i−2+2i0023−2300−2i2i0000−2ζ4+2ζ142ζ4−2ζ14−2ζ20+2ζ222ζ20−2ζ22−2ζ4−2ζ142ζ4+2ζ14−2ζ20−2ζ222ζ20+2ζ22000000000000000000000000000000000000
χ784-44-4-20004i−4i02-22−2i32i3−2i32i3000000000000−2−2i2+2i−2+2i2−2i0023−2300−2i2i00002ζ4−2ζ14−2ζ4+2ζ142ζ20−2ζ22−2ζ20+2ζ222ζ4+2ζ14−2ζ4−2ζ142ζ20+2ζ22−2ζ20−2ζ22000000000000000000000000000000000000
χ794-44-4-20004i−4i02-222i3−2i32i3−2i30000000000002+2i−2−2i2−2i−2+2i00−232300−2i2i0000−2ζ20+2ζ222ζ20−2ζ22−2ζ4+2ζ142ζ4−2ζ14−2ζ20−2ζ222ζ20+2ζ22−2ζ4−2ζ142ζ4+2ζ14000000000000000000000000000000000000
χ804-44-4-20004i−4i02-222i3−2i32i3−2i3000000000000−2−2i2+2i−2+2i2−2i00−232300−2i2i00002ζ20−2ζ22−2ζ20+2ζ222ζ4−2ζ14−2ζ4+2ζ142ζ20+2ζ22−2ζ20−2ζ222ζ4+2ζ14−2ζ4−2ζ14000000000000000000000000000000000000
χ814-44-4-2000−4i4i02-22−2i32i3−2i32i30000000000002−2i−2+2i2+2i−2−2i00−2323002i−2i0000−2ζ4−2ζ142ζ4+2ζ14−2ζ20−2ζ222ζ20+2ζ22−2ζ4+2ζ142ζ4−2ζ14−2ζ20+2ζ222ζ20−2ζ22000000000000000000000000000000000000
χ824-44-4-2000−4i4i02-22−2i32i3−2i32i3000000000000−2+2i2−2i−2−2i2+2i00−2323002i−2i00002ζ4+2ζ14−2ζ4−2ζ142ζ20+2ζ22−2ζ20−2ζ222ζ4−2ζ14−2ζ4+2ζ142ζ20−2ζ22−2ζ20+2ζ22000000000000000000000000000000000000
χ834-44-4-2000−4i4i02-222i3−2i32i3−2i30000000000002−2i−2+2i2+2i−2−2i0023−23002i−2i0000−2ζ20−2ζ222ζ20+2ζ22−2ζ4−2ζ142ζ4+2ζ14−2ζ20+2ζ222ζ20−2ζ22−2ζ4+2ζ142ζ4−2ζ14000000000000000000000000000000000000
χ844-44-4-2000−4i4i02-222i3−2i32i3−2i3000000000000−2+2i2−2i−2−2i2+2i0023−23002i−2i00002ζ20+2ζ22−2ζ20−2ζ222ζ4+2ζ14−2ζ4−2ζ142ζ20−2ζ22−2ζ20+2ζ222ζ4−2ζ14−2ζ4+2ζ14000000000000000000000000000000000000
χ854-4-44404i−4i000-4-444i−4i−4i4i000000000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ864-4-44404i−4i000-4-444i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ874-4-4440−4i4i000-4-44−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ884-4-4440−4i4i000-4-44−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ898-8-88-408i−8i00044-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88-40−8i8i00044-44i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.