Finite Group Databasebeta

← Group #10591190

Character table — Group #10591190

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size1111222222222222222244444444444444444444444444412121212121212121212121224242424242436363636
order122222334466666612121212346666666666612121212121212121212121212128888242424242424242444121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-1-1111111111111111-1-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11-111-1-111-1-1
χ61111-1-1111111111111111-1-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-11-1-111-1-111
χ71111-1-1111111111111111-1-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-111-1-1-1-111111-111-1-1-1-111
χ81111-1-1111111111111111-1-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-11-1-11111-1-1
χ922222222-2-2222222-2-2-2-22-222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000
χ102222222-12222-12-1-12222-1222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000
χ112222222-12222-12-1-12222-1222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-211110000
χ122222222-1-2-222-12-1-1-2-2-2-2-1-222-1-1-1-1-1-1-1-1-1-2-211111111111100000000000000−i3i3−i3i30000
χ132222222-1-2-222-12-1-1-2-2-2-2-1-222-1-1-1-1-1-1-1-1-1-2-211111111111100000000000000i3−i3i3−i30000
χ14222222-1222-1-12-122-1-1-1-1-12-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ15222222-1222-1-12-122-1-1-1-1-12-1-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ16222222-12-2-2-1-12-1221111-1-2-1-122-1-1-1-1-1-1-111-2-2-2-211111111000033−3−333−3−30000000000
χ17222222-12-2-2-1-12-1221111-1-2-1-122-1-1-1-1-1-1-111-2-2-2-2111111110000−3−333−3−3330000000000
χ182222-2-222-2-2222222-2-2-2-222-2-2-2-222-2-2-2-2222-2-222-2-2-2-222220000000000000000000000
χ192222-2-22-12222-12-1-12222-1-2-2-211-1-11111-1-2-2-1-111-1-1-1-111110000000000002-2-1-1110000
χ202222-2-22-12222-12-1-12222-1-2-2-211-1-11111-1-2-2-1-111-1-1-1-11111000000000000-2211-1-10000
χ212222-2-22-1-2-222-12-1-1-2-2-2-2-12-2-211-1-11111-12211-1-11111-1-1-1-100000000000000−i3i3i3−i30000
χ222222-2-22-1-2-222-12-1-1-2-2-2-2-12-2-211-1-11111-12211-1-11111-1-1-1-100000000000000i3−i3−i3i30000
χ232222-2-2-1222-1-12-122-1-1-1-1-1-211-2-2-1-11111-11122-2-2-1-1-1-1111122-2-2-1-1-1-111110000000000
χ242222-2-2-1222-1-12-122-1-1-1-1-1-211-2-2-1-11111-11122-2-2-1-1-1-11111-2-2221111-1-1-1-10000000000
χ252222-2-2-12-2-2-1-12-1221111-1211-2-2-1-11111-1-1-1-2-2221111-1-1-1-1000033−3−3−3−3330000000000
χ262222-2-2-12-2-2-1-12-1221111-1211-2-2-1-11111-1-1-1-2-2221111-1-1-1-10000−3−33333−3−30000000000
χ2722-2-22-222002-22-2-2-20000202-22-22-222-2-2-2000000000000002−22−22−22−22−22−20000000000
χ2822-2-22-222002-22-2-2-20000202-22-22-222-2-2-200000000000000−22−22−22−22−22−220000000000
χ2922-2-22-2-1200-1121-2-233−3−3-10-112-2-11-1-11113−3000033−3−333−3−32−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ3022-2-22-2-1200-1121-2-233−3−3-10-112-2-11-1-11113−3000033−3−333−3−3−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ3122-2-22-2-1200-1121-2-2−3−333-10-112-2-11-1-1111−330000−3−333−3−3332−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ3222-2-22-2-1200-1121-2-2−3−333-10-112-2-11-1-1111−330000−3−333−3−333−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ3322-2-2-2222002-22-2-2-2000020-22-222-2-2-222-2000000000000002−2−222−22−2−22−220000000000
χ3422-2-2-2222002-22-2-2-2000020-22-222-2-2-222-200000000000000−222−2−22−222−22−20000000000
χ3522-2-2-22-1200-1121-2-233−3−3-101-1-22-1111-1-11−33000033−3−3−3−3332−2−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ3622-2-2-22-1200-1121-2-233−3−3-101-1-22-1111-1-11−33000033−3−3−3−333−222−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ3722-2-2-22-1200-1121-2-2−3−333-101-1-22-1111-1-113−30000−3−33333−3−32−2−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ3822-2-2-22-1200-1121-2-2−3−333-101-1-22-1111-1-113−30000−3−33333−3−3−222−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ392-2-2200222-2-2-2-22-222-22-2200000-2-200002002-2002-22-20000000000000000000000002-2
χ402-2-2200222-2-2-2-22-222-22-2200000-2-200002002-2002-22-2000000000000000000000000-22
χ412-2-220022-22-2-2-22-22-22-22200000-2-20000200-2200-22-2200000000000000000000002-200
χ422-2-220022-22-2-2-22-22-22-22200000-2-20000200-2200-22-220000000000000000000000-2200
χ43444444-2-244-2-2-2-2-2-2-2-2-2-214-2-2-2-21111111-2-2-2-2-2-2111111110000000000000000000000
χ44444444-2-2-4-4-2-2-2-2-2-222221-4-2-2-2-21111111222222-1-1-1-1-1-1-1-10000000000000000000000
χ454444-4-4-2-244-2-2-2-2-2-2-2-2-2-21-4222211-1-1-1-1122-2-2221111-1-1-1-10000000000000000000000
χ464444-4-4-2-2-4-4-2-2-2-2-2-2222214222211-1-1-1-11-2-222-2-2-1-1-1-111110000000000000000000000
χ4744-4-44-44-2004-4-2-4220000-204-4-22-22-2-2222000000000000000000000000000000000000
χ4844-4-44-4-2-200-22-22222323−23−2310-22-221-111-1-1-123−230000−3−333−3−3330000000000000000000000
χ4944-4-44-4-2-200-22-2222−23−23232310-22-221-111-1-1-1−2323000033−3−333−3−30000000000000000000000
χ5044-4-4-444-2004-4-2-4220000-20-442-2-2222-2-22000000000000000000000000000000000000
χ5144-4-4-44-2-200-22-22222323−23−23102-22-21-1-1-111-1−23230000−3−33333−3−30000000000000000000000
χ5244-4-4-44-2-200-22-2222−23−232323102-22-21-1-1-111-123−23000033−3−3−3−3330000000000000000000000
χ534-44-4004400-44-4-44-40000400000-440000-4000000000000000000000000000000000000
χ544-44-4004-200-442-4-220000-2000002-200002000023−23000023−2323−230000000000000000000000
χ554-44-4004-200-442-4-220000-2000002-2000020000−23230000−2323−23230000000000000000000000
χ564-44-400-24002-2-424-423−23−2323-2000002-20000200000023−23−232300000000000000000000000000
χ574-44-400-24002-2-424-4−232323−23-2000002-200002000000−232323−2300000000000000000000000000
χ584-44-400-2-2002-222-2223−23−2323100000-113-33-3-1000023−23−333−3−33−330000000000000000000000
χ594-44-400-2-2002-222-2223−23−2323100000-11-33-33-10000−2323−333−33−33−30000000000000000000000
χ604-44-400-2-2002-222-22−232323−23100000-113-33-3-10000−23233−3−333−33−30000000000000000000000
χ614-44-400-2-2002-222-22−232323−23100000-11-33-33-1000023−233−3−33−33−330000000000000000000000
χ624-4-44004-24-4-4-4242-24-44-4-200000220000-200-2200-22-2200000000000000000000000000
χ634-4-44004-2-44-4-4242-2-44-44-200000220000-2002-2002-22-200000000000000000000000000
χ644-4-4400-244-422-4-2-44-22-22-200000220000-2004-400-22-2200000000000000000000000000
χ654-4-4400-24-4422-4-2-442-22-2-200000220000-200-44002-22-200000000000000000000000000
χ664-4-4400-2-24-4222-22-2-22-22100000-1-13-3-33100-22001-11-1-333-30000000000000000000000
χ674-4-4400-2-24-4222-22-2-22-22100000-1-1-333-3100-22001-11-13-3-330000000000000000000000
χ684-4-4400-2-2-44222-22-22-22-2100000-1-13-3-331002-200-11-113-3-330000000000000000000000
χ694-4-4400-2-2-44222-22-22-22-2100000-1-1-333-31002-200-11-11-333-30000000000000000000000

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