Finite Group Databasebeta

← Group #10696750

Character table — Group #10696750

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order1222344446662444466121212121212121288881212242424242424242422446666121212128888248888
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-11-111-1-111-1-11111-1-111-1-1
χ6111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-111-1-111
χ7111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-11-1-111-1-1111111-1-1-1-111
χ8111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-11111-1-1
χ9222222222222-22-2-2-2-2-222-2-222-2-200002-2000000000000000000000000002-200
χ10222222222222-22-2-2-2-2-222-2-222-2-200002-200000000000000000000000000-2200
χ112222222-2-22222-2-22-222-2-2-2-222220000-2-200000000020-2002200-2-20000000000
χ122222222-2-22222-2-22-222-2-2-2-222220000-2-2000000000-20200-2-200220000000000
χ132222222-2-2222-2-22-22-2-2-2-22222-2-20000-220000000000000000000000002-20000
χ142222222-2-2222-2-22-22-2-2-2-22222-2-20000-22000000000000000000000000-220000
χ1522222-2-2222222-2-2-222222-2-2-2-2-2-20000-2200000000000000000000000000002-2
χ1622222-2-2222222-2-2-222222-2-2-2-2-2-20000-220000000000000000000000000000-22
χ1722222-2-222222-2-222-2-2-22222-2-22222-2-2-2-22222-2-2-2-20000000000000000000000
χ1822222-2-222222-2-222-2-2-22222-2-222-2-222-2-2-2-2-2-222220000000000000000000000
χ1922222-2-2-2-2222222-2-222-2-222-2-2-2-200002-2000000000000000000002i2i−2i−2i000000
χ2022222-2-2-2-2222222-2-222-2-222-2-2-2-200002-200000000000000000000−2i−2i2i2i000000
χ2122222-2-2-2-2222-22-222-2-2-2-2-2-2-2-2220000220000000020-202200-2-2000000000000
χ2222222-2-2-2-2222-22-222-2-2-2-2-2-2-2-22200002200000000-2020-2-20022000000000000
χ232222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ242222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ252222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111112-22-2-1-111-1-1110000000000
χ262222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-22-2211-1-111-1-10000000000
χ272222-122-2-2-1-1-12-2-22-2-1-11111-1-1-1-1000011−i3−i3i3i3−i3−i3i3i3020-2−i3i3-1-1−i3i3110000000000
χ282222-122-2-2-1-1-12-2-22-2-1-11111-1-1-1-1000011−i3−i3i3i3−i3−i3i3i30-202i3−i311i3−i3-1-10000000000
χ292222-122-2-2-1-1-12-2-22-2-1-11111-1-1-1-1000011i3i3−i3−i3i3i3−i3−i3020-2i3−i3-1-1i3−i3110000000000
χ302222-122-2-2-1-1-12-2-22-2-1-11111-1-1-1-1000011i3i3−i3−i3i3i3−i3−i30-202−i3i311−i3i3-1-10000000000
χ312222-1-2-222-1-1-1-2-222-211-1-1-1-111-1-122-2-211-1-1-1-111110000−i3i3−i3i3i3−i3−i3i30000000000
χ322222-1-2-222-1-1-1-2-222-211-1-1-1-111-1-122-2-211-1-1-1-111110000i3−i3i3−i3−i3i3i3−i30000000000
χ332222-1-2-222-1-1-1-2-222-211-1-1-1-111-1-1-2-222111111-1-1-1-10000−i3i3i3−i3i3−i3i3−i30000000000
χ342222-1-2-222-1-1-1-2-222-211-1-1-1-111-1-1-2-222111111-1-1-1-10000i3−i3−i3i3−i3i3−i3i30000000000
χ352222-1-2-2-2-2-1-1-1-22-22211111111-1-10000-1-1−i3−i3i3i3i3i3−i3−i320-20-1-1−i3i311i3−i30000000000
χ362222-1-2-2-2-2-1-1-1-22-22211111111-1-10000-1-1−i3−i3i3i3i3i3−i3−i3-202011i3−i3-1-1−i3i30000000000
χ372222-1-2-2-2-2-1-1-1-22-22211111111-1-10000-1-1i3i3−i3−i3−i3−i3i3i320-20-1-1i3−i311−i3i30000000000
χ382222-1-2-2-2-2-1-1-1-22-22211111111-1-10000-1-1i3i3−i3−i3−i3−i3i3i3-202011−i3i3-1-1i3−i30000000000
χ394444-24444-2-2-2-44-4-4-422-2-222-2-2220000-22000000000000000000000000000000
χ404444-244-4-4-2-2-2-4-44-442222-2-2-2-22200002-2000000000000000000000000000000
χ414444-2-4-444-2-2-24-4-4-44-2-2-2-222222200002-2000000000000000000000000000000
χ424444-2-4-4-4-4-2-2-2444-4-4-2-222-2-222220000-22000000000000000000000000000000
χ4344-4-44004i−4i4-4-400000004i−4i000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ4444-4-44004i−4i4-4-400000004i−4i00000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ4544-4-4400−4i4i4-4-40000000−4i4i00000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ4644-4-4400−4i4i4-4-40000000−4i4i000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ474-44-444-400-4-44000000000004-4002-22-2002-22-22-22-20000000000000000000000
χ484-44-444-400-4-44000000000004-400-22-2200-22-22-22-220000000000000000000000
χ494-44-44-4400-4-4400000000000-44002-2-22002-22-2-22-220000000000000000000000
χ504-44-44-4400-4-4400000000000-4400-222-200-22-222-22-20000000000000000000000
χ514-44-4-24-40022-200000−2i32i30000-22−2i32i32-22-200−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i30000000000000000000000
χ524-44-4-24-40022-200000−2i32i30000-22−2i32i3-22-22001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i30000000000000000000000
χ534-44-4-24-40022-2000002i3−2i30000-222i3−2i32-22-200−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i30000000000000000000000
χ544-44-4-24-40022-2000002i3−2i30000-222i3−2i3-22-22001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i30000000000000000000000
χ554-44-4-2-440022-200000−2i32i300002-22i3−2i32-2-2200−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i30000000000000000000000
χ564-44-4-2-440022-200000−2i32i300002-22i3−2i3-222-2001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i30000000000000000000000
χ574-44-4-2-440022-2000002i3−2i300002-2−2i32i32-2-2200−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i30000000000000000000000
χ584-44-4-2-440022-2000002i3−2i300002-2−2i32i3-222-2001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i30000000000000000000000
χ5988-8-8-4008i−8i-4440000000−4i4i000000000000000000000000000000000000000000
χ6088-8-8-400−8i8i-44400000004i−4i000000000000000000000000000000000000000000
χ618-8-8880000-88-8000000000000000000000000000000000000000000000000000
χ628-8-88-400004-4400000000043−430000000000000000000000000000000000000000
χ638-8-88-400004-44000000000−43430000000000000000000000000000000000000000

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