Finite Group Databasebeta

← Group #10696216

Character table — Group #10696216

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order1222344446662444466121212121212121222446666121212121212888824242424242424248888244488
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111
χ5111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-11-11-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-11-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1
χ9222222222222-2-2-22-2-2-222-2-222-2-2000000002-2000000000000000022-2-2000000
χ10222222222222-2-2-22-2-2-222-2-222-2-2000000002-20000000000000000-2-222000000
χ112222222-2-222222-2-2-2222222-2-2-2-200000000-2-200002i−2i002i2i−2i−2i00000000000000
χ122222222-2-222222-2-2-2222222-2-2-2-200000000-2-20000−2i2i00−2i−2i2i2i00000000000000
χ132222222-2-2222-2-22-22-2-222-2-2-2-22200000000-2200000000000000000000020-200
χ142222222-2-2222-2-22-22-2-222-2-2-2-22200000000-22000000000000000000000-20200
χ1522222-2-2222222-22-2-222-2-2-2-2222200000000-2-20000002-2000022-2-20000000000
χ1622222-2-2222222-22-2-222-2-2-2-2222200000000-2-2000000-220000-2-2220000000000
χ1722222-2-222222-22-2-22-2-2-2-22222-2-200000000-220000000000000000000000002-2
χ1822222-2-222222-22-2-22-2-2-2-22222-2-200000000-22000000000000000000000000-22
χ1922222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-222-2-2222222-2-2-2-20000000000000000000000
χ2022222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222220000000000000000000000
χ2122222-2-2-2-2222-2222-2-2-2-2-222-2-222000000002-20000000000000000000020-2000
χ2222222-2-2-2-2222-2222-2-2-2-2-222-2-222000000002-200000000000000000000-202000
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
χ252222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-1111122-2-2-1-1-1-111110000000000
χ262222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-11111-2-2221111-1-1-1-10000000000
χ272222-122-2-2-1-1-122-2-2-2-1-1-1-1-1-111110000−i3−i3i3i311−i3−i3i3i32i−2i00−i−iii3−33−30000000000
χ282222-122-2-2-1-1-122-2-2-2-1-1-1-1-1-111110000−i3−i3i3i311−i3−i3i3i3−2i2i00ii−i−i−33−330000000000
χ292222-122-2-2-1-1-122-2-2-2-1-1-1-1-1-111110000i3i3−i3−i311i3i3−i3−i32i−2i00−i−iii−33−330000000000
χ302222-122-2-2-1-1-122-2-2-2-1-1-1-1-1-111110000i3i3−i3−i311i3i3−i3−i3−2i2i00ii−i−i3−33−30000000000
χ312222-1-2-222-1-1-12-22-2-2-1-11111-1-1-1-10000−i3−i3i3i311i3i3−i3−i3002-2−i3i3−i3i3-1-1110000000000
χ322222-1-2-222-1-1-12-22-2-2-1-11111-1-1-1-10000−i3−i3i3i311i3i3−i3−i300-22i3−i3i3−i311-1-10000000000
χ332222-1-2-222-1-1-12-22-2-2-1-11111-1-1-1-10000i3i3−i3−i311−i3−i3i3i3002-2i3−i3i3−i3-1-1110000000000
χ342222-1-2-222-1-1-12-22-2-2-1-11111-1-1-1-10000i3i3−i3−i311−i3−i3i3i300-22−i3i3−i3i311-1-10000000000
χ352222-1-2-2-2-2-1-1-12-2-222-1-11111111122-2-2-1-1-1-1-1-1111100003−3−333−3−330000000000
χ362222-1-2-2-2-2-1-1-12-2-222-1-11111111122-2-2-1-1-1-1-1-111110000−333−3−333−30000000000
χ372222-1-2-2-2-2-1-1-12-2-222-1-111111111-2-2221111-1-1-1-1-1-100003−3−33−333−30000000000
χ382222-1-2-2-2-2-1-1-12-2-222-1-111111111-2-2221111-1-1-1-1-1-10000−333−33−3−330000000000
χ394444-24444-2-2-2-4-4-44-422-2-222-2-22200000000-2200000000000000000000000000
χ404444-244-4-4-2-2-2-4-44-4422-2-22222-2-2000000002-200000000000000000000000000
χ414444-2-4-444-2-2-2-44-4-442222-2-2-2-222000000002-200000000000000000000000000
χ424444-2-4-4-4-4-2-2-2-4444-42222-2-222-2-200000000-2200000000000000000000000000
χ434-44-44004i−4i4-4-4000000000004i−4i002-22i−2i2-22-2002i−2i2i−2i0000000000000000000000
χ444-44-44004i−4i4-4-4000000000004i−4i00-22−2i2i-22-2200−2i2i−2i2i0000000000000000000000
χ454-44-4400−4i4i4-4-400000000000−4i4i002-2−2i2i2-22-200−2i2i−2i2i0000000000000000000000
χ464-44-4400−4i4i4-4-400000000000−4i4i00-222i−2i-22-22002i−2i2i−2i0000000000000000000000
χ474-44-4-2004i−4i-22200000−2i32i30000−2i2i23−232-22i−2i−1−i31+i3−1+i31−i3002ζ14−2ζ142ζ22−2ζ220000000000000000000000
χ484-44-4-2004i−4i-22200000−2i32i30000−2i2i23−23-22−2i2i1+i3−1−i31−i3−1+i300−2ζ142ζ14−2ζ222ζ220000000000000000000000
χ494-44-4-2004i−4i-222000002i3−2i30000−2i2i−23232-22i−2i−1+i31−i3−1−i31+i3002ζ22−2ζ222ζ14−2ζ140000000000000000000000
χ504-44-4-2004i−4i-222000002i3−2i30000−2i2i−2323-22−2i2i1−i3−1+i31+i3−1−i300−2ζ222ζ22−2ζ142ζ140000000000000000000000
χ514-44-4-200−4i4i-22200000−2i32i300002i−2i−23232-2−2i2i−1−i31+i3−1+i31−i300−2ζ142ζ14−2ζ222ζ220000000000000000000000
χ524-44-4-200−4i4i-22200000−2i32i300002i−2i−2323-222i−2i1+i3−1−i31−i3−1+i3002ζ14−2ζ142ζ22−2ζ220000000000000000000000
χ534-44-4-200−4i4i-222000002i3−2i300002i−2i23−232-2−2i2i−1+i31−i3−1−i31+i300−2ζ222ζ22−2ζ142ζ140000000000000000000000
χ544-44-4-200−4i4i-222000002i3−2i300002i−2i23−23-222i−2i1−i3−1+i31+i3−1−i3002ζ22−2ζ222ζ14−2ζ140000000000000000000000
χ554-4-4444-400-4-4400000004-4000000000000000000000000000000000022−22000000
χ564-4-4444-400-4-4400000004-40000000000000000000000000000000000−2222000000
χ574-4-444-4400-4-440000000-440000000000000000000000000000000022−2200000000
χ584-4-444-4400-4-440000000-4400000000000000000000000000000000−222200000000
χ5988-8-880000-88-8000000000000000000000000000000000000000000000000000
χ6088-8-8-400004-4400000000043−430000000000000000000000000000000000000000
χ6188-8-8-400004-44000000000−43430000000000000000000000000000000000000000
χ628-8-88-48-80044-40000000-44000000000000000000000000000000000000000000
χ638-8-88-4-880044-400000004-4000000000000000000000000000000000000000000

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