Finite Group Databasebeta

← Group #10693038

Character table — Group #10693038

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order1222223444444666121212124446688888888121212121212224466661212121212122424242424242424444444448888888888242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111111-1-1-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−i11-1-1-1-111-1-111111-1-1-1-1-1iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−ii−iii−i−i1-1i−i
χ101111111-1-1-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−i11-1-1-1-111-1-111111-1-1-1-1-1iiii−i−i−i−i-1-111-1-111−i−i−i−iiiiii−iii−i−i-11−ii
χ111111111-1-1-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−i11-1-1-1-1-1-111-1-1-1-11-11111iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i−ii−i−iii-11−ii
χ121111111-1-1-1-1-1-1111-1-1-1-1-11111iiii−i−i−i−i11-1-1-1-1-1-111-1-1-1-11-11111iiii−i−i−i−i-1-111-1-111−i−i−i−iiiii−ii−i−iii1-1i−i
χ131111111-1-1-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiii11-1-1-1-111-1-111111-1-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii−ii−i−iii1-1−ii
χ141111111-1-1-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiii11-1-1-1-111-1-111111-1-1-1-1-1−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i−ii−i−iii-11i−i
χ151111111-1-1-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiii11-1-1-1-1-1-111-1-1-1-11-11111−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiiii−iii−i−i-11i−i
χ161111111-1-1-1-1-1-1111-1-1-1-1-11111−i−i−i−iiiii11-1-1-1-1-1-111-1-1-1-11-11111−i−i−i−iiiii-1-111-1-111iiii−i−i−i−ii−iii−i−i1-1−ii
χ172222222222-2-222222222-2-2-22200000000-2-222-2-200000000-2-20000000000002222-2-2-2-2000000000000000000
χ182222222222-2-222222222-2-2-22200000000-2-222-2-200000000-2-2000000000000-2-2-2-22222000000000000000000
χ192222222-2-2-222-2222-2-2-2-22-2-22200000000-2-2-2-22200000000-2200000000000022-2-2-2-222000000000000000000
χ202222222-2-2-222-2222-2-2-2-22-2-22200000000-2-2-2-22200000000-22000000000000-2-22222-2-2000000000000000000
χ21222222-1222222-1-1-1-1-1-1-1222-1-122222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ22222222-1222222-1-1-1-1-1-1-1222-1-122222222-1-1-1-1-1-1-2-2-2-21111-1-11111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-2-2-2-21111-1-1111111111111000000000000000022-1-1-1-10000
χ25222222-1-2-2-2-2-2-2-1-1-11111-222-1-12i2i2i2i−2i−2i−2i−2i-1-1111122-2-2-1-1-1-1-111111−i−i−i−iiiii00000000000000002i−2i−i−iii0000
χ26222222-1-2-2-2-2-2-2-1-1-11111-222-1-12i2i2i2i−2i−2i−2i−2i-1-11111-2-2221111-11-1-1-1-1−i−i−i−iiiii0000000000000000−2i2iii−i−i0000
χ27222222-1-2-2-2-2-2-2-1-1-11111-222-1-1−2i−2i−2i−2i2i2i2i2i-1-1111122-2-2-1-1-1-1-111111iiii−i−i−i−i0000000000000000−2i2iii−i−i0000
χ28222222-1-2-2-2-2-2-2-1-1-11111-222-1-1−2i−2i−2i−2i2i2i2i2i-1-11111-2-2221111-11-1-1-1-1iiii−i−i−i−i00000000000000002i−2i−i−iii0000
χ292222-2-222-2222-22222222-22-2-2-222-2-222-2-222-2-22200000000-2-2000022-2-222-2-200000000000000000000000000
χ302222-2-222-2222-22222222-22-2-2-2-2-222-2-22222-2-22200000000-2-20000-2-222-2-22200000000000000000000000000
χ312222-2-222-22-2-2-222222222-22-2-200000000-2-2-2-2-2-20000000022000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ322222-2-222-22-2-2-222222222-22-2-200000000-2-2-2-2-2-2000000002200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ332222-2-22-22-2222222-2-2-2-2-2-22-2-200000000-2-22222000000002-20000000000000000000022-2-2-2-2220000000000
χ342222-2-22-22-2222222-2-2-2-2-2-22-2-200000000-2-22222000000002-200000000000000000000-2-22222-2-20000000000
χ352222-2-22-22-2-2-22222-2-2-2-222-2-2-22i2i−2i−2i−2i−2i2i2i2222-2-200000000-2200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ362222-2-22-22-2-2-22222-2-2-2-222-2-2-2−2i−2i2i2i2i2i−2i−2i2222-2-200000000-220000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ372222-2-2-12-2222-2-1-1-1-1-1-1-1-22-21122-2-222-2-2-1-111-1-10000−i3−i3i3i311−i3−i3i3i3-1-111-1-111000000000000000000−i3i3−i3i30000
χ382222-2-2-12-2222-2-1-1-1-1-1-1-1-22-21122-2-222-2-2-1-111-1-10000i3i3−i3−i311i3i3−i3−i3-1-111-1-111000000000000000000i3−i3i3−i30000
χ392222-2-2-12-2222-2-1-1-1-1-1-1-1-22-211-2-222-2-222-1-111-1-10000−i3−i3i3i311−i3−i3i3i311-1-111-1-1000000000000000000i3−i3i3−i30000
χ402222-2-2-12-2222-2-1-1-1-1-1-1-1-22-211-2-222-2-222-1-111-1-10000i3i3−i3−i311i3i3−i3−i311-1-111-1-1000000000000000000−i3i3−i3i30000
χ412222-2-2-1-22-2-2-22-1-1-1111122-2112i2i−2i−2i−2i−2i2i2i-1-1-1-1110000−i3−i3i3i31-1i3i3−i3−i3−i−iiiii−i−i0000000000000000003−3−330000
χ422222-2-2-1-22-2-2-22-1-1-1111122-2112i2i−2i−2i−2i−2i2i2i-1-1-1-1110000i3i3−i3−i31-1−i3−i3i3i3−i−iiiii−i−i000000000000000000−333−30000
χ432222-2-2-1-22-2-2-22-1-1-1111122-211−2i−2i2i2i2i2i−2i−2i-1-1-1-1110000−i3−i3i3i31-1i3i3−i3−i3ii−i−i−i−iii000000000000000000−333−30000
χ442222-2-2-1-22-2-2-22-1-1-1111122-211−2i−2i2i2i2i2i−2i−2i-1-1-1-1110000i3i3−i3−i31-1−i3−i3i3i3ii−i−i−i−iii0000000000000000003−3−330000
χ452-2-222-222-2-2002-2-2222-2-20002-2−i2i2−i2i2−i2i2−i2i2002-20000000000000000−i2i2−i2i2−i2i2−i2i22i−2i2i−2i00002−22−22−22−20000000000
χ462-2-222-222-2-2002-2-2222-2-20002-2−i2i2−i2i2−i2i2−i2i2002-20000000000000000−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i0000−22−22−22−220000000000
χ472-2-222-222-2-2002-2-2222-2-20002-2i2−i2i2−i2i2−i2i2−i2002-20000000000000000i2−i2i2−i2i2−i2i2−i22i−2i2i−2i0000−22−22−22−220000000000
χ482-2-222-222-2-2002-2-2222-2-20002-2i2−i2i2−i2i2−i2i2−i2002-20000000000000000i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i00002−22−22−22−20000000000
χ492-2-222-22-22200-2-2-22-2-2220002-22−22−2−22−2200-2200000000000000002−22−2−22−222i−2i−2i2i0000i2−i2i2−i2−i2i2−i2i20000000000
χ502-2-222-22-22200-2-2-22-2-2220002-22−22−2−22−2200-2200000000000000002−22−2−22−22−2i2i2i−2i0000−i2i2−i2i2i2−i2i2−i20000000000
χ512-2-222-22-22200-2-2-22-2-2220002-2−22−222−22−200-220000000000000000−22−222−22−22i−2i−2i2i0000−i2i2−i2i2i2−i2i2−i20000000000
χ522-2-222-22-22200-2-2-22-2-2220002-2−22−222−22−200-220000000000000000−22−222−22−2−2i2i2i−2i0000i2−i2i2−i2−i2i2−i2i20000000000
χ532-2-22-22222-200-2-2-2222-2-2000-22−i2i2i2−i2−i2i2i2−i200-220000000000000000−i2i2i2−i2−i2i2i2−i200002-22-2−i2i2i2−i2−i2i2i2−i20000000000
χ542-2-22-22222-200-2-2-2222-2-2000-22−i2i2i2−i2−i2i2i2−i200-220000000000000000−i2i2i2−i2−i2i2i2−i20000-22-22i2−i2−i2i2i2−i2−i2i20000000000
χ552-2-22-22222-200-2-2-2222-2-2000-22i2−i2−i2i2i2−i2−i2i200-220000000000000000i2−i2−i2i2i2−i2−i2i200002-22-2i2−i2−i2i2i2−i2−i2i20000000000
χ562-2-22-22222-200-2-2-2222-2-2000-22i2−i2−i2i2i2−i2−i2i200-220000000000000000i2−i2−i2i2i2−i2−i2i20000-22-22−i2i2i2−i2−i2i2i2−i20000000000
χ572-2-22-222-2-22002-2-22-2-222000-222−2−22−222−2002-200000000000000002−2−22−222−200002-2-222−2−22−222−20000000000
χ582-2-22-222-2-22002-2-22-2-222000-222−2−22−222−2002-200000000000000002−2−22−222−20000-222-2−222−22−2−220000000000
χ592-2-22-222-2-22002-2-22-2-222000-22−222−22−2−22002-20000000000000000−222−22−2−2200002-2-22−222−22−2−220000000000
χ602-2-22-222-2-22002-2-22-2-222000-22−222−22−2−22002-20000000000000000−222−22−2−220000-222-22−2−22−222−20000000000
χ61444444-2444-4-44-2-2-2-2-2-2-2-4-4-4-2-20000000022-2-222000000002200000000000000000000000000000000000000
χ62444444-2-4-4-444-4-2-2-222224-4-4-2-2000000002222-2-2000000002-200000000000000000000000000000000000000
χ634444-4-4-24-44-4-4-4-2-2-2-2-2-2-24-44220000000022222200000000-2-200000000000000000000000000000000000000
χ644444-4-4-2-44-4444-2-2-22222-4-44220000000022-2-2-2-200000000-2200000000000000000000000000000000000000
χ654-44-40040004i−4i04-4-40000000000000000000004i−4i2-22i−2i2-22-2002i−2i2i−2i0000000000000000000000000000000000
χ664-44-40040004i−4i04-4-40000000000000000000004i−4i-22−2i2i-22-2200−2i2i−2i2i0000000000000000000000000000000000
χ674-44-4004000−4i4i04-4-4000000000000000000000−4i4i2-2−2i2i2-22-200−2i2i−2i2i0000000000000000000000000000000000
χ684-44-4004000−4i4i04-4-4000000000000000000000−4i4i-222i−2i-22-22002i−2i2i−2i0000000000000000000000000000000000
χ694-44-400-20004i−4i0-22223−2323−230000000000000−2i32i300−2i2i2-22i−2i−1−i31+i3−1+i31−i3002ζ22−2ζ222ζ14−2ζ140000000000000000000000000000000000
χ704-44-400-20004i−4i0-22223−2323−230000000000000−2i32i300−2i2i-22−2i2i1+i3−1−i31−i3−1+i300−2ζ222ζ22−2ζ142ζ140000000000000000000000000000000000
χ714-44-400-20004i−4i0-222−2323−232300000000000002i3−2i300−2i2i2-22i−2i−1+i31−i3−1−i31+i3002ζ14−2ζ142ζ22−2ζ220000000000000000000000000000000000
χ724-44-400-20004i−4i0-222−2323−232300000000000002i3−2i300−2i2i-22−2i2i1−i3−1+i31+i3−1−i300−2ζ142ζ14−2ζ222ζ220000000000000000000000000000000000
χ734-44-400-2000−4i4i0-22223−2323−2300000000000002i3−2i3002i−2i2-2−2i2i−1+i31−i3−1−i31+i300−2ζ142ζ14−2ζ222ζ220000000000000000000000000000000000
χ744-44-400-2000−4i4i0-22223−2323−2300000000000002i3−2i3002i−2i-222i−2i1−i3−1+i31+i3−1−i3002ζ14−2ζ142ζ22−2ζ220000000000000000000000000000000000
χ754-44-400-2000−4i4i0-222−2323−23230000000000000−2i32i3002i−2i2-2−2i2i−1−i31+i3−1+i31−i300−2ζ222ζ22−2ζ142ζ140000000000000000000000000000000000
χ764-44-400-2000−4i4i0-222−2323−23230000000000000−2i32i3002i−2i-222i−2i1+i3−1−i31−i3−1+i3002ζ22−2ζ222ζ14−2ζ140000000000000000000000000000000000
χ774-4-444-4-24-4-400422-2-2-222000-22−2i22i2−2i22i2−2i22i2−2i22i200-220000000000000000i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ784-4-444-4-24-4-400422-2-2-222000-222i2−2i22i2−2i22i2−2i22i2−2i200-220000000000000000−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ794-4-444-4-2-44400-422-222-2-2000-2222−2222−22−2222−2222002-20000000000000000−22−222−22−200000000000000000000000000
χ804-4-444-4-2-44400-422-222-2-2000-22−2222−222222−2222−22002-200000000000000002−22−2−22−2200000000000000000000000000
χ814-4-44-44-244-400-422-2-2-2220002-2−2i22i22i2−2i2−2i22i22i2−2i2002-20000000000000000i2−i2−i2i2i2−i2−i2i200000000000000000000000000
χ824-4-44-44-244-400-422-2-2-2220002-22i2−2i2−2i22i22i2−2i2−2i22i2002-20000000000000000−i2i2i2−i2−i2i2i2−i200000000000000000000000000
χ834-4-44-44-2-4-4400422-222-2-20002-222−22−2222−222222−2200-220000000000000000−222−22−2−2200000000000000000000000000
χ844-4-44-44-2-4-4400422-222-2-20002-2−222222−2222−22−222200-2200000000000000002−2−22−222−200000000000000000000000000
χ8588-8-8008000000-88-800000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-40000004-4443−43−43430000000000000000000000000000000000000000000000000000000000000000000
χ8788-8-800-40000004-44−434343−430000000000000000000000000000000000000000000000000000000000000000000

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