Finite Group Databasebeta

← Group #10692765

Character table — Group #10692765

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222224444444444444444444444444444444444448888888888888888888888888824242424484848484848
order122222344446661212121244446688888888121212121212242424242424242424242424242424242444668888121212121212121224242424242424248888244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1
χ41111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ6111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ91111-1-11-1-1-1-1111-1-1-1-111-11-1-1ii−i−iii−i−i1111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111i−ii−i1-111-1-1-1-1ii−i−iii−i−i11-1-11-1i−ii−i
χ101111-1-11-1-1-1-1111-1-1-1-111-11-1-1ii−i−iii−i−i1111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111i−ii−i1-111-1-1-1-1ii−i−iii−i−i-1-111-11−ii−ii
χ111111-1-11-1-1-1-1111-1-1-1-111-11-1-1ii−i−i−i−iii1111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1i−i−ii1-1-1-11111ii−i−i−i−iii11-1-1-11i−i−ii
χ121111-1-11-1-1-1-1111-1-1-1-111-11-1-1ii−i−i−i−iii1111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1i−i−ii1-1-1-11111ii−i−i−i−iii-1-1111-1−iii−i
χ131111-1-11-1-1-1-1111-1-1-1-111-11-1-1−i−iiiii−i−i1111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1−iii−i1-1-1-11111−i−iiiii−i−i11-1-1-11−iii−i
χ141111-1-11-1-1-1-1111-1-1-1-111-11-1-1−i−iiiii−i−i1111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1−iii−i1-1-1-11111−i−iiiii−i−i-1-1111-1i−i−ii
χ151111-1-11-1-1-1-1111-1-1-1-111-11-1-1−i−iii−i−iii1111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111−ii−ii1-111-1-1-1-1−i−iii−i−iii11-1-11-1−ii−ii
χ161111-1-11-1-1-1-1111-1-1-1-111-11-1-1−i−iii−i−iii1111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111−ii−ii1-111-1-1-1-1−i−iii−i−iii-1-111-11i−ii−i
χ17222222222-2-222222222-2-2-2220000222222-2-2-2-2000000002222222200000000-2-2-2-20000000000-2-2-2-20000000000
χ18222222222-2-222222222-2-2-2220000-2-2-2-222-2-2-2-200000000-2-2-2-2-2-2-2-20000000022-2-2000000000022220000000000
χ192222222-2-222222-2-2-2-2-2-2-222200000000-2-2-2-22200000000000000002-2-222200002-2-2-222-2-2000000000000000000
χ202222222-2-222222-2-2-2-2-2-2-222200000000-2-2-2-2220000000000000000-222-2-2-200002-222-2-222000000000000000000
χ212222222-2-2-2-2222-2-2-2-2-222-2222i2i−2i−2i0000-2-222-2-22i2i2i2i−2i−2i−2i−2i00000000000000−2i2i00-22000000−2i−2i2i2i00000000000000
χ222222222-2-2-2-2222-2-2-2-2-222-222−2i−2i2i2i0000-2-222-2-2−2i−2i−2i−2i2i2i2i2i000000000000002i−2i00-220000002i2i−2i−2i00000000000000
χ23222222-12222-1-1-1-1-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ24222222-12222-1-1-1-1-1-1-12222-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-21122-2-2-1-1111111-1-1-1-111110000000000
χ25222222-12222-1-1-1-1-1-1-12222-1-1-2-2-2-22222-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-2-2-2-211-2-222-1-11111111111-1-1-1-10000000000
χ26222222-12222-1-1-1-1-1-1-12222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111111111112222-1-1-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000
χ27222222-122-2-2-1-1-1-1-1-1-12-2-2-2-1-100002222-1-11111−i3−i3i3i3−i3−i3i3i3-1-1-1-1-1-1-1-10000−i3i300-2-211−i3i3−i3i3−i3i3−i3i3−i3i311110000000000
χ28222222-122-2-2-1-1-1-1-1-1-12-2-2-2-1-100002222-1-11111i3i3−i3−i3i3i3−i3−i3-1-1-1-1-1-1-1-10000i3−i300-2-211i3−i3i3−i3i3−i3i3−i3i3−i311110000000000
χ29222222-122-2-2-1-1-1-1-1-1-12-2-2-2-1-10000-2-2-2-2-1-11111−i3−i3i3i3−i3−i3i3i3111111110000i3−i3002211i3−i3i3−i3i3−i3−i3i3−i3i3-1-1-1-10000000000
χ30222222-122-2-2-1-1-1-1-1-1-12-2-2-2-1-10000-2-2-2-2-1-11111i3i3−i3−i3i3i3−i3−i3111111110000−i3i3002211−i3i3−i3i3−i3i3i3−i3i3−i3-1-1-1-10000000000
χ31222222-1-2-222-1-1-11111-2-2-22-1-1000000001111-1-133−3−3−3−33333−3−333−3−32-2-22-1-10000-1111-1-111−333−33−33−30000000000
χ32222222-1-2-222-1-1-11111-2-2-22-1-1000000001111-1-133−3−3−3−333−3−333−3−333-222-2110000-11-1-111-1-1−333−3−33−330000000000
χ33222222-1-2-222-1-1-11111-2-2-22-1-1000000001111-1-1−3−33333−3−333−3−333−3−3-222-2110000-11-1-111-1-13−3−333−33−30000000000
χ34222222-1-2-222-1-1-11111-2-2-22-1-1000000001111-1-1−3−33333−3−3−3−333−3−3332-2-22-1-10000-1111-1-1113−3−33−33−330000000000
χ35222222-1-2-2-2-2-1-1-11111-222-2-1-12i2i−2i−2i000011-1-111−i−i−i−iiiii33−3−333−3−30000−i3i3−2i2i001-1i3−i3−i3i3i3−i3ii−i−i−33−330000000000
χ36222222-1-2-2-2-2-1-1-11111-222-2-1-12i2i−2i−2i000011-1-111−i−i−i−iiiii−3−333−3−3330000i3−i3−2i2i001-1−i3i3i3−i3−i3i3ii−i−i3−33−30000000000
χ37222222-1-2-2-2-2-1-1-11111-222-2-1-1−2i−2i2i2i000011-1-111iiii−i−i−i−i33−3−333−3−30000i3−i32i−2i001-1−i3i3i3−i3−i3i3−i−iii−33−330000000000
χ38222222-1-2-2-2-2-1-1-11111-222-2-1-1−2i−2i2i2i000011-1-111iiii−i−i−i−i−3−333−3−3330000−i3i32i−2i001-1i3−i3−i3i3i3−i3−i−iii3−33−30000000000
χ392222-2-2222222222222-22-2-2-2-222220000-2-222222222222200000000000000-2-200-2-2000000-2-2-2-200000000000000
χ402222-2-2222222222222-22-2-2-2-2-2-2-2-20000-2-22222-2-2-2-2-2-2-2-2000000000000002200-2-2000000222200000000000000
χ412222-2-2222-2-22222222-2-222-2-200000000-2-2-2-2-2-200000000000000002-22-222000022-2-2-2-222000000000000000000
χ422222-2-2222-2-22222222-2-222-2-200000000-2-2-2-2-2-20000000000000000-22-22-2-20000222222-2-2000000000000000000
χ432222-2-22-2-222222-2-2-2-22-22-2-2-200002i2i−2i−2i22-2-222000000002i2i2i2i−2i−2i−2i−2i00000000−2i2i-220000000000−2i−2i2i2i0000000000
χ442222-2-22-2-222222-2-2-2-22-22-2-2-20000−2i−2i2i2i22-2-22200000000−2i−2i−2i−2i2i2i2i2i000000002i−2i-2200000000002i2i−2i−2i0000000000
χ452222-2-2-12222-1-1-1-1-1-1-1-22-2-2112222000011-1-1-1-1-1-1-1-1-1-1-1-1−i3−i3i3i3i3i3−i3−i30000−i3i3-2-20011i3−i3i3−i3−i3i31111i3−i3−i3i30000000000
χ462222-2-2-12222-1-1-1-1-1-1-1-22-2-2112222000011-1-1-1-1-1-1-1-1-1-1-1-1i3i3−i3−i3−i3−i3i3i30000i3−i3-2-20011−i3i3−i3i3i3−i31111−i3i3i3−i30000000000
χ472222-2-2-12222-1-1-1-1-1-1-1-22-2-211-2-2-2-2000011-1-1-1-111111111−i3−i3i3i3i3i3−i3−i30000i3−i3220011−i3i3−i3i3i3−i3-1-1-1-1i3−i3−i3i30000000000
χ482222-2-2-12222-1-1-1-1-1-1-1-22-2-211-2-2-2-2000011-1-1-1-111111111i3i3−i3−i3−i3−i3i3i30000−i3i3220011i3−i3i3−i3−i3i3-1-1-1-1−i3i3i3−i30000000000
χ492222-2-2-122-2-2-1-1-1-1-1-1-1-2-2221100000000111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i32-22-2-1-10000-1-11111-1-1i3−i3i3−i3−i3i3i3−i30000000000
χ502222-2-2-122-2-2-1-1-1-1-1-1-1-2-2221100000000111111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-22-22110000-1-1-1-1-1-111i3−i3i3−i3i3−i3−i3i30000000000
χ512222-2-2-122-2-2-1-1-1-1-1-1-1-2-2221100000000111111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-22-22110000-1-1-1-1-1-111−i3i3−i3i3−i3i3i3−i30000000000
χ522222-2-2-122-2-2-1-1-1-1-1-1-1-2-2221100000000111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i32-22-2-1-10000-1-11111-1-1−i3i3−i3i3i3−i3−i3i30000000000
χ532222-2-2-1-2-222-1-1-111112-22-21100002i2i−2i−2i-1-111-1-133−3−3−3−333−i−i−i−iiiii0000−i3i300−2i2i1-1−i3i3i3−i3i3−i33−3−33ii−i−i0000000000
χ542222-2-2-1-2-222-1-1-111112-22-21100002i2i−2i−2i-1-111-1-1−3−33333−3−3−i−i−i−iiiii0000i3−i300−2i2i1-1i3−i3−i3i3−i3i3−333−3ii−i−i0000000000
χ552222-2-2-1-2-222-1-1-111112-22-2110000−2i−2i2i2i-1-111-1-133−3−3−3−333iiii−i−i−i−i0000i3−i3002i−2i1-1i3−i3−i3i3−i3i33−3−33−i−iii0000000000
χ562222-2-2-1-2-222-1-1-111112-22-2110000−2i−2i2i2i-1-111-1-1−3−33333−3−3iiii−i−i−i−i0000−i3i3002i−2i1-1−i3i3i3−i3i3−i3−333−3−i−iii0000000000
χ572222-2-2-1-2-2-2-2-1-1-1111122-22112i2i−2i−2i2i2i−2i−2i-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii22-2-2-1-12i−2i2i−2i-11-1-11111−i−iii−i−iii0000000000
χ582222-2-2-1-2-2-2-2-1-1-1111122-22112i2i−2i−2i−2i−2i2i2i-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-2-222112i−2i−2i2i-1111-1-1-1-1−i−iiiii−i−i0000000000
χ592222-2-2-1-2-2-2-2-1-1-1111122-2211−2i−2i2i2i2i2i−2i−2i-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-2-22211−2i2i2i−2i-1111-1-1-1-1ii−i−i−i−iii0000000000
χ602222-2-2-1-2-2-2-2-1-1-1111122-2211−2i−2i2i2i−2i−2i2i2i-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i22-2-2-1-1−2i2i−2i2i-11-1-11111ii−i−iii−i−i0000000000
χ6144-4-4004004i−4i4-4-400000000002+2i−2−2i2−2i−2+2i000000004i−4i2+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i00000000000000000000000000000000000000000000
χ6244-4-4004004i−4i4-4-40000000000−2−2i2+2i−2+2i2−2i000000004i−4i−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i00000000000000000000000000000000000000000000
χ6344-4-400400−4i4i4-4-400000000002−2i−2+2i2+2i−2−2i00000000−4i4i2−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i00000000000000000000000000000000000000000000
χ6444-4-400400−4i4i4-4-40000000000−2+2i2−2i−2−2i2+2i00000000−4i4i−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i00000000000000000000000000000000000000000000
χ6544-4-400-2004i−4i-222−2i3−2i32i32i30000002+2i−2−2i2−2i−2+2i00000023−23−2i2i−2ζ4+2ζ142ζ4−2ζ14−2ζ20+2ζ222ζ20−2ζ22−2ζ4−2ζ142ζ4+2ζ14−2ζ20−2ζ222ζ20+2ζ2200000000000000000000000000000000000000000000
χ6644-4-400-2004i−4i-222−2i3−2i32i32i3000000−2−2i2+2i−2+2i2−2i00000023−23−2i2i2ζ4−2ζ14−2ζ4+2ζ142ζ20−2ζ22−2ζ20+2ζ222ζ4+2ζ14−2ζ4−2ζ142ζ20+2ζ22−2ζ20−2ζ2200000000000000000000000000000000000000000000
χ6744-4-400-2004i−4i-2222i32i3−2i3−2i30000002+2i−2−2i2−2i−2+2i000000−2323−2i2i−2ζ20+2ζ222ζ20−2ζ22−2ζ4+2ζ142ζ4−2ζ14−2ζ20−2ζ222ζ20+2ζ22−2ζ4−2ζ142ζ4+2ζ1400000000000000000000000000000000000000000000
χ6844-4-400-2004i−4i-2222i32i3−2i3−2i3000000−2−2i2+2i−2+2i2−2i000000−2323−2i2i2ζ20−2ζ22−2ζ20+2ζ222ζ4−2ζ14−2ζ4+2ζ142ζ20+2ζ22−2ζ20−2ζ222ζ4+2ζ14−2ζ4−2ζ1400000000000000000000000000000000000000000000
χ6944-4-400-200−4i4i-222−2i3−2i32i32i30000002−2i−2+2i2+2i−2−2i000000−23232i−2i−2ζ4−2ζ142ζ4+2ζ14−2ζ20−2ζ222ζ20+2ζ22−2ζ4+2ζ142ζ4−2ζ14−2ζ20+2ζ222ζ20−2ζ2200000000000000000000000000000000000000000000
χ7044-4-400-200−4i4i-222−2i3−2i32i32i3000000−2+2i2−2i−2−2i2+2i000000−23232i−2i2ζ4+2ζ14−2ζ4−2ζ142ζ20+2ζ22−2ζ20−2ζ222ζ4−2ζ14−2ζ4+2ζ142ζ20−2ζ22−2ζ20+2ζ2200000000000000000000000000000000000000000000
χ7144-4-400-200−4i4i-2222i32i3−2i3−2i30000002−2i−2+2i2+2i−2−2i00000023−232i−2i−2ζ20−2ζ222ζ20+2ζ22−2ζ4−2ζ142ζ4+2ζ14−2ζ20+2ζ222ζ20−2ζ22−2ζ4+2ζ142ζ4−2ζ1400000000000000000000000000000000000000000000
χ7244-4-400-200−4i4i-2222i32i3−2i3−2i3000000−2+2i2−2i−2−2i2+2i00000023−232i−2i2ζ20+2ζ22−2ζ20−2ζ222ζ4+2ζ14−2ζ4−2ζ142ζ20−2ζ22−2ζ20+2ζ222ζ4−2ζ14−2ζ4+2ζ1400000000000000000000000000000000000000000000
χ734-44-40044i−4i00-44-44i−4i4i−4i000000000000000000000000000000000000000000000000000000000000002-22i−2i000000
χ744-44-40044i−4i00-44-44i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000-22−2i2i000000
χ754-44-4004−4i4i00-44-4−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000002-2−2i2i000000
χ764-44-4004−4i4i00-44-4−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000-222i−2i000000
χ774-4-444-440000-4-44000000004-40000−2i22i2−2i22i200000000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000
χ784-4-444-440000-4-44000000004-400002i2−2i22i2−2i2000000000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000
χ794-4-444-4-2000022-223−23−23230000-220000−2i22i2−2i22i223−230000000000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23000000000000000000000000000000000000
χ804-4-444-4-2000022-223−23−23230000-2200002i2−2i22i2−2i223−23000000000000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23000000000000000000000000000000000000
χ814-4-444-4-2000022-2−232323−230000-220000−2i22i2−2i22i2−23230000000000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7000000000000000000000000000000000000
χ824-4-444-4-2000022-2−232323−230000-2200002i2−2i22i2−2i2−2323000000000000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7000000000000000000000000000000000000
χ834-4-44-4440000-4-4400000000-44000022−22−22220000000000000022−2222−22−2222−2222000000000000000000000000000000000000
χ844-4-44-4440000-4-4400000000-440000−222222−2200000000000000−2222−222222−2222−22000000000000000000000000000000000000
χ854-4-44-44-2000022-223−23−232300002-2000022−22−2222−23230000000000002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23000000000000000000000000000000000000
χ864-4-44-44-2000022-223−23−232300002-20000−222222−22−2323000000000000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23000000000000000000000000000000000000
χ874-4-44-44-2000022-2−232323−2300002-2000022−22−222223−230000000000002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000000000000000
χ884-4-44-44-2000022-2−232323−2300002-20000−222222−2223−23000000000000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ72ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000000000000000
χ898-88-800-48i−8i004-44−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-800-4−8i8i004-444i−4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000

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