Finite Group Databasebeta

← Group #10696756

Character table — Group #10696756

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order122234444666244441212121212121212121268888122424242424242424888824242424242424248888222444
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111
χ51111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-11-1-11-1
χ61111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-111-11
χ71111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11-1-11
χ81111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-111-1
χ9222222222222-22-2-2-222-2-222-2-2-2-2-200002000000002-20022-2-200000000000000
χ10222222222222-22-2-2-222-2-222-2-2-2-2-20000200000000-2200-2-22200000000000000
χ112222222-2-22222-2-2-22-2-2-2-22222-2-220000-200000000000000000000000000200-2
χ122222222-2-22222-2-2-22-2-2-2-22222-2-220000-200000000000000000000000000-2002
χ132222222-2-2222-2-222-2-2-22222-2-222-20000-2000000000000000000000000200-200
χ142222222-2-2222-2-222-2-2-22222-2-222-20000-2000000000000000000000000-200200
χ1522222-2-2222222-2-22-222-2-2-2-2-2-22220000-200000000002-2000022-2-20000000000
χ1622222-2-2222222-2-22-222-2-2-2-2-2-22220000-20000000000-220000-2-2220000000000
χ1722222-2-222222-2-22-222222-2-222-2-2-222-2-2-22222-2-2-2-20000000000000000000000
χ1822222-2-222222-2-22-222222-2-222-2-2-2-2-222-2-2-2-2-222220000000000000000000000
χ1922222-2-2-2-2222222-2-2-2-222-2-2-2-2-2-2200002000000000000000000002i2i−2i−2i000000
χ2022222-2-2-2-2222222-2-2-2-222-2-2-2-2-2-220000200000000000000000000−2i−2i2i2i000000
χ2122222-2-2-2-2222-22-222-2-2-2-2-2-22222-2000020000000000000000000000000200-20
χ2222222-2-2-2-2222-22-222-2-2-2-2-2-22222-2000020000000000000000000000000-20020
χ232222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ242222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ252222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-11111111122-2-2-1-1-1-111110000000000
χ262222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-111111111-2-2221111-1-1-1-10000000000
χ272222-12222-1-1-1-22-2-2-2-1-111-1-1111110000-133−3−333−3−32-200-1-1113−33−30000000000
χ282222-12222-1-1-1-22-2-2-2-1-111-1-1111110000-133−3−333−3−3-220011-1-1−33−330000000000
χ292222-12222-1-1-1-22-2-2-2-1-111-1-1111110000-1−3−333−3−3332-200-1-111−33−330000000000
χ302222-12222-1-1-1-22-2-2-2-1-111-1-1111110000-1−3−333−3−333-220011-1-13−33−30000000000
χ312222-1-2-222-1-1-12-2-22-2-1-1111111-1-1-10000133−3−3−3−333002-23−33−3-1-1110000000000
χ322222-1-2-222-1-1-12-2-22-2-1-1111111-1-1-10000133−3−3−3−33300-22−33−3311-1-10000000000
χ332222-1-2-222-1-1-12-2-22-2-1-1111111-1-1-100001−3−33333−3−3002-2−33−33-1-1110000000000
χ342222-1-2-222-1-1-12-2-22-2-1-1111111-1-1-100001−3−33333−3−300-223−33−311-1-10000000000
χ352222-1-2-222-1-1-1-2-22-22-1-1-1-111-1-111122-2-21-1-1-1-1111100003−3−33−333−30000000000
χ362222-1-2-222-1-1-1-2-22-22-1-1-1-111-1-111122-2-21-1-1-1-111110000−333−33−3−330000000000
χ372222-1-2-222-1-1-1-2-22-22-1-1-1-111-1-1111-2-22211111-1-1-1-100003−3−333−3−330000000000
χ382222-1-2-222-1-1-1-2-22-22-1-1-1-111-1-1111-2-22211111-1-1-1-10000−333−3−333−30000000000
χ394444-244-4-4-2-2-24-4-4-442222-2-2-2-222-200002000000000000000000000000000000
χ404444-244-4-4-2-2-2-4-444-422-2-2-2-222-2-2200002000000000000000000000000000000
χ414444-2-4-4-4-4-2-2-2444-4-422-2-2222222-20000-2000000000000000000000000000000
χ424444-2-4-4-4-4-2-2-2-44-444222222-2-2-2-220000-2000000000000000000000000000000
χ4344-4-44004i−4i4-4-4000004i−4i00000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ4444-4-44004i−4i4-4-4000004i−4i0000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ4544-4-4400−4i4i4-4-400000−4i4i0000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ4644-4-4400−4i4i4-4-400000−4i4i00000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ474-4-4444-400-44-40000000004-4000002-22-202-22-22-22-20000000000000000000000
χ484-4-4444-400-44-40000000004-400000-22-220-22-22-22-220000000000000000000000
χ494-4-444-4400-44-4000000000-44000002-2-2202-22-2-22-220000000000000000000000
χ504-4-444-4400-44-4000000000-4400000-222-20-22-222-22-20000000000000000000000
χ514-4-44-24-4002-22000000023−23-220023−2302-22-20−1+31−3−1−31+3−1+31−3−1−31+30000000000000000000000
χ524-4-44-24-4002-22000000023−23-220023−230-22-2201−3−1+31+3−1−31−3−1+31+3−1−30000000000000000000000
χ534-4-44-24-4002-220000000−2323-2200−232302-22-20−1−31+3−1+31−3−1−31+3−1+31−30000000000000000000000
χ544-4-44-24-4002-220000000−2323-2200−23230-22-2201+3−1−31−3−1+31+3−1−31−3−1+30000000000000000000000
χ554-4-44-2-44002-22000000023−232-200−232302-2-220−1+31−3−1−31+31−3−1+31+3−1−30000000000000000000000
χ564-4-44-2-44002-22000000023−232-200−23230-222-201−3−1+31+3−1−3−1+31−3−1−31+30000000000000000000000
χ574-4-44-2-44002-220000000−23232-20023−2302-2-220−1−31+3−1+31−31+3−1−31−3−1+30000000000000000000000
χ584-4-44-2-44002-220000000−23232-20023−230-222-201+3−1−31−3−1+3−1−31+3−1+31−30000000000000000000000
χ5988-8-8-4008i−8i-44400000−4i4i00000000000000000000000000000000000000000000
χ6088-8-8-400−8i8i-444000004i−4i00000000000000000000000000000000000000000000
χ618-88-880000-8-88000000000000000000000000000000000000000000000000000
χ628-88-8-4000044-40000000000043−4300000000000000000000000000000000000000
χ638-88-8-4000044-400000000000−434300000000000000000000000000000000000000

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