Finite Group Databasebeta

← Group #10692295

Character table — Group #10692295

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121212121212161616161616161616162424242448484848
order12223444444666244466121212121212121288888888121224242424242424242244888844121212122424242444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ911111-11-1-1-111111-11-111-1-1-111-1-1-1ii−i−iii−i−i-11iiii−i−i−i−i11-1-1ii−i−i1-111-1-1ii−i−i-11i−ii−i1-1
χ1011111-11-1-1-111111-11-111-1-1-111-1-1-1ii−i−iii−i−i-11iiii−i−i−i−i-1-111−i−iii1-111-1-1ii−i−i1-1−ii−ii-11
χ1111111-11-1-1-111111-11-111-1-1-111-1-1-1ii−i−i−i−iii-11−i−i−i−iiiii11-1-1ii−i−i-11-1-111ii−i−i-11i−i−ii-11
χ1211111-11-1-1-111111-11-111-1-1-111-1-1-1ii−i−i−i−iii-11−i−i−i−iiiii-1-111−i−iii-11-1-111ii−i−i1-1−iii−i1-1
χ1311111-11-1-1-111111-11-111-1-1-111-1-1-1−i−iiiii−i−i-11iiii−i−i−i−i11-1-1−i−iii-11-1-111−i−iii-11−iii−i-11
χ1411111-11-1-1-111111-11-111-1-1-111-1-1-1−i−iiiii−i−i-11iiii−i−i−i−i-1-111ii−i−i-11-1-111−i−iii1-1i−i−ii1-1
χ1511111-11-1-1-111111-11-111-1-1-111-1-1-1−i−iii−i−iii-11−i−i−i−iiiii11-1-1−i−iii1-111-1-1−i−iii-11−ii−ii1-1
χ1611111-11-1-1-111111-11-111-1-1-111-1-1-1−i−iii−i−iii-11−i−i−i−iiiii-1-111ii−i−i1-111-1-1−i−iii1-1i−ii−i-11
χ172222222-2-222222-2-2-22-2-222-22222-200000000-2-20000000022-2-2000000000000002-2000000
χ182222222-2-222222-2-2-22-2-222-22222-200000000-2-200000000-2-22200000000000000-22000000
χ19222222-2222-2222-2-22-2-2-2222-2-2-2-2200000000-220000000000002222000000000000-2-20000
χ20222222-2222-2222-2-22-2-2-2222-2-2-2-2200000000-22000000000000-2-2-2-2000000000000220000
χ21222222-2-2-22-222222-2-22222-2-2-2-2-2-22i−2i2i−2i00002-200000000000000000000002i−2i2i−2i00000000
χ22222222-2-2-22-222222-2-22222-2-2-2-2-2-2−2i2i−2i2i00002-20000000000000000000000−2i2i−2i2i00000000
χ2322222-2222-22222-22-2-2-2-2-2-2222-2-22000000002-200000000222200000000000000-2-2000000
χ2422222-2222-22222-22-2-2-2-2-2-2222-2-22000000002-200000000-2-2-2-20000000000000022000000
χ2522222-2-222-2-22222-2-2222-2-22-2-22222-2-220000-2-200000000000000000000002-2-2200000000
χ2622222-2-222-2-22222-2-2222-2-22-2-2222-222-20000-2-20000000000000000000000-222-200000000
χ2722222-2-2-2-2-2-2222-2222-2-2-2-2-2-2-222-200000000220000000000002i2i−2i−2i000000000000−2i2i0000
χ2822222-2-2-2-2-2-2222-2222-2-2-2-2-2-2-222-20000000022000000000000−2i−2i2i2i0000000000002i−2i0000
χ292222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-100000000
χ302222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-11111111100000000-2-21111-1-1-1-100000000
χ312222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-100000000-2-21111111100000000
χ322222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000000022-1-1-1-1111100000000
χ332222-12-2-2-22-2-1-1-122-2-2-1-1-1-11111112i−2i2i−2i0000-1133−3−333−3−30000000000−i3i3−i3i3−ii−ii00000000
χ342222-12-2-2-22-2-1-1-122-2-2-1-1-1-11111112i−2i2i−2i0000-11−3−333−3−3330000000000i3−i3i3−i3−ii−ii00000000
χ352222-12-2-2-22-2-1-1-122-2-2-1-1-1-1111111−2i2i−2i2i0000-1133−3−333−3−30000000000i3−i3i3−i3i−ii−i00000000
χ362222-12-2-2-22-2-1-1-122-2-2-1-1-1-1111111−2i2i−2i2i0000-11−3−333−3−3330000000000−i3i3−i3i3i−ii−i00000000
χ372222-1-22-2-2-22-1-1-12-22-2-1-1111-1-11112i2i−2i−2i2i2i−2i−2i1-1−i−i−i−iiiii000000002-2-1-111−i−iii00000000
χ382222-1-22-2-2-22-1-1-12-22-2-1-1111-1-11112i2i−2i−2i−2i−2i2i2i1-1iiii−i−i−i−i00000000-2211-1-1−i−iii00000000
χ392222-1-22-2-2-22-1-1-12-22-2-1-1111-1-1111−2i−2i2i2i2i2i−2i−2i1-1−i−i−i−iiiii00000000-2211-1-1ii−i−i00000000
χ402222-1-22-2-2-22-1-1-12-22-2-1-1111-1-1111−2i−2i2i2i−2i−2i2i2i1-1iiii−i−i−i−i000000002-2-1-111ii−i−i00000000
χ412222-1-2-222-2-2-1-1-12-2-22-1-111-111-1-1-12-2-22000011−i3−i3i3i3i3i3−i3−i30000000000−i3i3i3−i3-111-100000000
χ422222-1-2-222-2-2-1-1-12-2-22-1-111-111-1-1-12-2-22000011i3i3−i3−i3−i3−i3i3i30000000000i3−i3−i3i3-111-100000000
χ432222-1-2-222-2-2-1-1-12-2-22-1-111-111-1-1-1-222-2000011−i3−i3i3i3i3i3−i3−i30000000000i3−i3−i3i31-1-1100000000
χ442222-1-2-222-2-2-1-1-12-2-22-1-111-111-1-1-1-222-2000011i3i3−i3−i3−i3−i3i3i30000000000−i3i3i3−i31-1-1100000000
χ454444-244-4-444-2-2-2-4-4-4422-2-22-2-2-2-2200000000220000000000000000000000000000000000
χ464444-24-4444-4-2-2-2-4-44-422-2-2-22222-2000000002-20000000000000000000000000000000000
χ474444-2-4444-44-2-2-2-44-4-42222-2-2-222-200000000-220000000000000000000000000000000000
χ484444-2-4-4-4-4-4-4-2-2-2-44442222222-2-2200000000-2-20000000000000000000000000000000000
χ4944-4-44004-4004-4-40000000040000-400002-22-2002-22-22-22-200000000000000000000000000
χ5044-4-44004-4004-4-40000000040000-40000-22-2200-22-22-22-2200000000000000000000000000
χ5144-4-4400-44004-4-400000000-40000400002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ5244-4-4400-44004-4-400000000-4000040000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5344-4-4-2004-400-2220000−2i32i300-200−2i32i3200002-22-200−1−i31+i3−1+i31−i3−1+i31−i3−1−i31+i300000000000000000000000000
χ5444-4-4-2004-400-2220000−2i32i300-200−2i32i320000-22-22001+i3−1−i31−i3−1+i31−i3−1+i31+i3−1−i300000000000000000000000000
χ5544-4-4-2004-400-22200002i3−2i300-2002i3−2i3200002-22-200−1+i31−i3−1−i31+i3−1−i31+i3−1+i31−i300000000000000000000000000
χ5644-4-4-2004-400-22200002i3−2i300-2002i3−2i320000-22-22001−i3−1+i31+i3−1−i31+i3−1−i31−i3−1+i300000000000000000000000000
χ5744-4-4-200-4400-2220000−2i32i3002002i3−2i3-200002i−2i−2i2i002ζ22−2ζ222ζ14−2ζ14−2ζ142ζ14−2ζ222ζ2200000000000000000000000000
χ5844-4-4-200-4400-2220000−2i32i3002002i3−2i3-20000−2i2i2i−2i00−2ζ222ζ22−2ζ142ζ142ζ14−2ζ142ζ22−2ζ2200000000000000000000000000
χ5944-4-4-200-4400-22200002i3−2i300200−2i32i3-200002i−2i−2i2i002ζ14−2ζ142ζ22−2ζ22−2ζ222ζ22−2ζ142ζ1400000000000000000000000000
χ6044-4-4-200-4400-22200002i3−2i300200−2i32i3-20000−2i2i2i−2i00−2ζ142ζ14−2ζ222ζ222ζ22−2ζ222ζ14−2ζ1400000000000000000000000000
χ614-44-444000-40-44-40000004-4000000000000000000000000000022−2222−22000000000000000000
χ624-44-444000-40-44-40000004-40000000000000000000000000000−2222−2222000000000000000000
χ634-44-44-400040-44-4000000-440000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ644-44-44-400040-44-4000000-4400000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ654-4-44404000-4-4-440000000004-4000000000000000000000004i−4i0000000000000000000000
χ664-4-44404000-4-4-440000000004-400000000000000000000000−4i4i0000000000000000000000
χ674-4-4440-40004-4-44000000000-440000000000000000000004-4000000000000000000000000
χ684-4-4440-40004-4-44000000000-44000000000000000000000-44000000000000000000000000
χ698-88-8-48000-804-44000000-4400000000000000000000000000000000000000000000000000
χ708-88-8-4-8000804-440000004-400000000000000000000000000000000000000000000000000
χ718-8-88-408000-844-4000000000-4400000000000000000000000000000000000000000000000
χ728-8-88-40-8000844-40000000004-400000000000000000000000000000000000000000000000

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