Finite Group Databasebeta

← Group #13138866

Character table — Group #13138866

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111122222222224444446666666612121212121212121212121212121212121212121212121212121212181836363636363636363636363636363672727272727272727272
order122234466612121212882424242433666666366612121212121212122424242424242424242424242424242444224448812121212242424244466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111
χ511111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-11111-1-1-1-111-1-1-1-11111
χ711111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-11111-1111-1-1-1-111
χ811111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1-1
χ9222222222222222222222-12-1-122-1-1-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10022000000000000020-1-100-1-100
χ10222222222222222222222-12-1-122-1-1-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-20000000000000-2011001100
χ1122222222222222222222-12-122-1-12-1-1-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000002200000000000200-1-100-1-1
χ1222222222222222222222-12-122-1-12-1-1-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000-2-200000000000-200110011
χ1322222222222222-2-2-2-2-2-22-12-1-122-1-1-1-1-12-1-1-12-1-1-1-2-2-2-211111111111100220000000000000-20-1-1001100
χ1422222222222222-2-2-2-2-2-22-12-1-122-1-1-1-1-12-1-1-12-1-1-1-2-2-2-211111111111100-2-20000000000000201100-1-100
χ1522222222222222-2-2-2-2-2-2-12-122-1-12-1-1-1-1-12-1-1-12-1-11111-2-2-2-211111111000002200000000000-200-1-10011
χ1622222222222222-2-2-2-2-2-2-12-122-1-12-1-1-1-1-12-1-1-12-1-11111-2-2-2-21111111100000-2-2000000000002001100-1-1
χ1722222-2-2222-2-2-2-2000000222222222222-2-2-2-2-2-2-2-200000000000000002200-2000022-2-200000000000000
χ1822222-2-2222-2-2-2-2000000222222222222-2-2-2-2-2-2-2-20000000000000000-2-20020000-2-22200000000000000
χ192-22-2200-22-20000−i2i2−i2−i2i2i222-22-22-2-222-2-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i22-200000−i2i22-200−i2−i2i2i20000000000
χ202-22-2200-22-20000−i2i2−i2−i2i2i222-22-22-2-222-2-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2-2200000i2−i2-2200i2i2−i2−i20000000000
χ212-22-2200-22-20000i2−i2i2i2−i2−i222-22-22-2-222-2-200000000i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i22-200000i2−i22-200i2i2−i2−i20000000000
χ222-22-2200-22-20000i2−i2i2i2−i2−i222-22-22-2-222-2-200000000i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2-2200000−i2i2-2200−i2−i2i2i20000000000
χ232-2-2222-22-2-222-2-200000022-2-2-2-2222-2-222222-2-2-2-20000000000000000000002i−2i000000000000002i−2i0000
χ242-2-2222-22-2-222-2-200000022-2-2-2-2222-2-222222-2-2-2-2000000000000000000000−2i2i00000000000000−2i2i0000
χ252-2-2222-22-2-222-2-2000000-121-2-21-12-111-1-12-1-11-2113−33−3000033−3−333−3−3000002i−2i00000000000000−ii00−i3i3
χ262-2-2222-22-2-222-2-2000000-121-2-21-12-111-1-12-1-11-2113−33−3000033−3−333−3−300000−2i2i00000000000000i−i00i3−i3
χ272-2-2222-22-2-222-2-2000000-121-2-21-12-111-1-12-1-11-211−33−330000−3−333−3−333000002i−2i00000000000000−ii00i3−i3
χ282-2-2222-22-2-222-2-2000000-121-2-21-12-111-1-12-1-11-211−33−330000−3−333−3−33300000−2i2i00000000000000i−i00−i3i3
χ292-2-222-222-2-2-2-22200000022-2-2-2-2222-2-22-2-2-2-222220000000000000000002-20000000000000002-2000000
χ302-2-222-222-2-2-2-22200000022-2-2-2-2222-2-22-2-2-2-22222000000000000000000-22000000000000000-22000000
χ312-2-222-222-2-2-2-2220000002-1-211-22-1-111-1-21112-1-1-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3002-2000000000000000-1100−i3i300
χ322-2-222-222-2-2-2-2220000002-1-211-22-1-111-1-21112-1-1-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300-220000000000000001-100i3−i300
χ332-2-222-222-2-2-2-2220000002-1-211-22-1-111-1-21112-1-1-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3002-2000000000000000-1100i3−i300
χ342-2-222-222-2-2-2-2220000002-1-211-22-1-111-1-21112-1-1-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300-220000000000000001-100−i3i300
χ3544444444444444444444-2-2-2-2-2-2-2-21111-2-211-2-211-2-2-2-2-2-2-2-211111111000000000000000000000000000
χ3644444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-21111-2-211-2-21122222222-1-1-1-1-1-1-1-1000000000000000000000000000
χ3744444-4-4444-4-4-4-40000004-24-2-244-2-2-2-2-2-4222-42220000000000000000000000000000000000000000000
χ3844444-4-4444-4-4-4-4000000-24-244-2-24-2-2-2-22-4222-4220000000000000000000000000000000000000000000
χ3944444-4-4444-4-4-4-4000000-2-2-2-2-2-2-2-2111122-1-122-1-1000000003i−3i−3i3i3i−3i−3i3i000000000000000000000000000
χ4044444-4-4444-4-4-4-4000000-2-2-2-2-2-2-2-2111122-1-122-1-100000000−3i3i3i−3i−3i3i3i−3i000000000000000000000000000
χ4144-4-4400-4-440000000000444-44-4-4-44-44-4000000000000000000000000000000000000000000000000000
χ4244-4-4400-4-4400000000004-242-2-4-42-22-220000000000006−6−666−66−6−66−66000000000000000000000000000
χ4344-4-4400-4-4400000000004-242-2-4-42-22-22000000000000−666−6−66−666−66−6000000000000000000000000000
χ4444-4-4400-4-440000000000-24-2-4422-4-22-2200000000i6−i6−i6i60000i6i6−i6−i6−i6−i6i6i6000000000000000000000000000
χ4544-4-4400-4-440000000000-24-2-4422-4-22-2200000000−i6i6i6−i60000−i6−i6i6i6i6i6−i6−i6000000000000000000000000000
χ4644-4-4400-4-440000000000-2-2-22-22221-11-1003i−3i003i−3ii6−i6−i6i66−6−66−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13000000000000000000000000000
χ4744-4-4400-4-440000000000-2-2-22-22221-11-1003i−3i003i−3i−i6i6i6−i6−666−6ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13000000000000000000000000000
χ4844-4-4400-4-440000000000-2-2-22-22221-11-100−3i3i00−3i3ii6−i6−i6i6−666−6−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23000000000000000000000000000
χ4944-4-4400-4-440000000000-2-2-22-22221-11-100−3i3i00−3i3i−i6i6i6−i66−6−66ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23000000000000000000000000000
χ504-44-4400-44-40000−2i22i2−2i2−2i22i22i24-2-4-224-42-2-22200000000−2i2−2i22i22i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2000000000000000000000000000
χ514-44-4400-44-40000−2i22i2−2i2−2i22i22i2-2424-4-22-4-2-22200000000i2i2−i2−i2−2i2−2i22i22i2i2i2i2i2−i2−i2−i2−i2000000000000000000000000000
χ524-44-4400-44-40000−2i22i2−2i2−2i22i22i2-2-22-22-22211-1-1003i−3i00−3i3ii2i2−i2−i2i2i2−i2−i2−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23000000000000000000000000000
χ534-44-4400-44-40000−2i22i2−2i2−2i22i22i2-2-22-22-22211-1-100−3i3i003i−3ii2i2−i2−i2i2i2−i2−i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23000000000000000000000000000
χ544-44-4400-44-400002i2−2i22i22i2−2i2−2i24-2-4-224-42-2-222000000002i22i2−2i2−2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2000000000000000000000000000
χ554-44-4400-44-400002i2−2i22i22i2−2i2−2i2-2424-4-22-4-2-22200000000−i2−i2i2i22i22i2−2i2−2i2−i2−i2−i2−i2i2i2i2i2000000000000000000000000000
χ564-44-4400-44-400002i2−2i22i22i2−2i2−2i2-2-22-22-22211-1-1003i−3i00−3i3i−i2−i2i2i2−i2−i2i2i22ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23000000000000000000000000000
χ574-44-4400-44-400002i2−2i22i22i2−2i2−2i2-2-22-22-22211-1-100−3i3i003i−3i−i2−i2i2i2−i2−i2i2i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23000000000000000000000000000
χ584-4-4444-44-4-444-4-40000004-2-422-44-2-222-24-2-2-2-42220000000000000000000000000000000000000000000
χ594-4-4444-44-4-444-4-4000000-2-22222-2-21-1-11-2-21122-1-123−2323−230000−3−333−3−333000000000000000000000000000
χ604-4-4444-44-4-444-4-4000000-2-22222-2-21-1-11-2-21122-1-1−2323−2323000033−3−333−3−3000000000000000000000000000
χ614-4-444-444-4-4-4-444000000-242-4-42-24-222-22-422-24-2-20000000000000000000000000000000000000000000
χ624-4-444-444-4-4-4-444000000-2-22222-2-21-1-1122-1-1-2-2110000−2i32i3−2i32i3i3−i3i3−i3i3−i3i3−i3000000000000000000000000000
χ634-4-444-444-4-4-4-444000000-2-22222-2-21-1-1122-1-1-2-21100002i3−2i32i3−2i3−i3i3−i3i3−i3i3−i3i3000000000000000000000000000
χ646666-366-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000220020022-1-1-1-1-1-1-1-10000000000
χ656666-366-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000-2-200-200-2-2111111110000000000
χ666666-366-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000002200200-2-2-1-1-1-111110000000000
χ676666-366-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000-2-200-200221111-1-1-1-10000000000
χ686666-3-6-6-3-3-333330033−3333−330000000000000000000000000000000000002200-20000-1-1113−33−30000000000
χ696666-3-6-6-3-3-333330033−3333−33000000000000000000000000000000000000-2-2002000011-1-1−33−330000000000
χ706666-3-6-6-3-3-3333300−3333−33330000000000000000000000000000000000002200-20000-1-111−33−330000000000
χ716666-3-6-6-3-3-3333300−3333−3333000000000000000000000000000000000000-2-2002000011-1-13−33−30000000000
χ726-66-6-3003-3333−3333−33−3i23i23ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ230000000000000000000000000000000000002-200000−i2i2-113−3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000
χ736-66-6-3003-3333−3333−33−3i23i23ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ23000000000000000000000000000000000000-2200000i2−i21-1−33−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000
χ746-66-6-3003-3333−3333−333i2−3i2−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ230000000000000000000000000000000000002-200000i2−i2-113−3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ230000000000
χ756-66-6-3003-3333−3333−333i2−3i2−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ23000000000000000000000000000000000000-2200000−i2i21-1−33ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ230000000000
χ766-66-6-3003-33−3333−3333−3i23i23ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ70000000000000000000000000000000000002-200000−i2i2-11−33ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000
χ776-66-6-3003-33−3333−3333−3i23i23ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ7000000000000000000000000000000000000-2200000i2−i21-13−3−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000
χ786-66-6-3003-33−3333−33333i2−3i2−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ70000000000000000000000000000000000002-200000i2−i2-11−33−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000
χ796-66-6-3003-33−3333−33333i2−3i2−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ7000000000000000000000000000000000000-2200000−i2i21-13−3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000
χ801212-12-12-60066-663−63−6363000000000000000000000000000000000000000000000000000000000000000000000
χ811212-12-12-60066-6−636363−63000000000000000000000000000000000000000000000000000000000000000000000
χ8212-12-1212-612-12-666-6-666000000000000000000000000000000000000000000000000000000000000000000000
χ8312-12-1212-6-1212-66666-6-6000000000000000000000000000000000000000000000000000000000000000000000

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