Finite Group Databasebeta

← Group #13167376

Character table — Group #13167376

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11222224444444444444888888888888888888818181818363636363636363636363636363636367272727272727272144144
order123468833661212122424242424243366121212121224242424242424242424241212246668881212242424242424248824242424612
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-11-1-11-1-1-1-111-1-1-1-111-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111-1-11-1-11-1-1-1-111-1-1-1-1-1-1111111-1-1
χ511111-1-11111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-1-1-1-1-11-11-111-1-11-1
χ611111-1-11111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-1-1-1-1-1-11-11-1-111-11
χ711111-1-11111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-111-1-1-1-111111-1-11-1-1111-1
χ811111-1-11111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-111-1-1-1-11111-111-111-1-1-11
χ9222222222222222222222222222222222222222-2-2-2-200-200-20000-2-200000000000000
χ1022222-2-22222222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200-200200002200000000000000
χ11222-22002222-2-2-20000002222-2-2-2-2-200000000002-2-2-20020002i−2i00002i2i−2i−2i0000000000
χ12222-22002222-2-2-20000002222-2-2-2-2-200000000002-2-2-2002000−2i2i0000−2i−2i2i2i0000000000
χ13222-22002222-2-2-20000002222-2-2-2-2-20000000000-22222-2-222000-2-20000000000000000
χ14222-22002222-2-2-20000002222-2-2-2-2-20000000000-2222-22-2-2-2000220000000000000000
χ1522-12-1222222-1222222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-100-10020000-1-100000022-1-1-1-100
χ1622-12-1222222-1222222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-100-10020000-1-1000000-2-2111100
χ1722-12-1222222-1222222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-21100100-2000011000000003−33−300
χ1822-12-1222222-1222222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-21100100-200001100000000−33−3300
χ1922-12-1-2-22222-122-2-2-2-211-1-1-1-12-1-1-1-1-2-21111111122-1-100-100-20000110000002-2-1-11100
χ2022-12-1-2-22222-122-2-2-2-211-1-1-1-12-1-1-1-1-2-21111111122-1-100-100-2000011000000-2211-1-100
χ2122-12-1-2-22222-122-2-2-2-211-1-1-1-12-1-1-1-1-2-211111111-2-2110010020000-1-1000000003−3−3300
χ2222-12-1-2-22222-122-2-2-2-211-1-1-1-12-1-1-1-1-2-211111111-2-2110010020000-1-100000000−333−300
χ2344444441-21-24111111441-21-2-211-2-2-2-21111-2-2-2-20000220-1-1022-1-100-1-1-1-10000000000
χ2444444441-21-24111111441-21-2-211-2-2-2-21111-2-2-2-20000-2-20110-2-2110011110000000000
χ254444444-21-214-2-2-2-2-2-244-21-211-2-21111-2-2-2-211110000000000000000000022000000-1-1
χ264444444-21-214-2-2-2-2-2-244-21-211-2-21111-2-2-2-2111100000000000000000000-2-200000011
χ2744444-4-41-21-2411-1-1-1-1-4-41-21-2-211-2-222-1-1-1-122220000220-1-10-2-2-1-10011110000000000
χ2844444-4-41-21-2411-1-1-1-1-4-41-21-2-211-2-222-1-1-1-122220000-2-20110221100-1-1-1-10000000000
χ2944444-4-4-21-214-2-22222-4-4-21-211-2-211-1-12222-1-1-1-1000000000000000000002-2000000-11
χ3044444-4-4-21-214-2-22222-4-4-21-211-2-211-1-12222-1-1-1-100000000000000000000-220000001-1
χ31444-44001-21-2-4-1-13i3i−3i−3i001-21-22-1-122003i3i−3i−3i000000002-20-1-102i−2i1100−i−iii0000000000
χ32444-44001-21-2-4-1-13i3i−3i−3i001-21-22-1-122003i3i−3i−3i00000000-220110−2i2i-1-100ii−i−i0000000000
χ33444-44001-21-2-4-1-1−3i−3i3i3i001-21-22-1-12200−3i−3i3i3i000000002-20-1-10−2i2i1100ii−i−i0000000000
χ34444-44001-21-2-4-1-1−3i−3i3i3i001-21-22-1-12200−3i−3i3i3i00000000-2201102i−2i-1-100−i−iii0000000000
χ3544-2-4-20044442-4-4000000-2-2-2-2-4222200000000004-42200-200000000000000000000000
χ3644-2-4-20044442-4-4000000-2-2-2-2-422220000000000-44-2-200200000000000000000000000
χ374-440-4−2i22i21-2-1203i−3i−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−2i22i21-2-1203i−3i00−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−i2−i2i2i20000000−i3i30003−300−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ384-440-4−2i22i21-2-1203i−3i−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−2i22i21-2-1203i−3i00−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−i2−i2i2i20000000i3−i3000−3300ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ394-440-4−2i22i21-2-120−3i3i2ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2i22i21-2-120−3i3i00−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−i2−i2i2i20000000−i3i3000−3300ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ404-440-4−2i22i21-2-120−3i3i2ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2i22i21-2-120−3i3i00−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−i2−i2i2i20000000i3−i30003−300−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ414-440-4−2i22i244-4-40002i2−2i2−2i22i2−2i22i244-4-4000002i2−2i22i2−2i2−2i22i22i22i2−2i2−2i2000000000000000000000000000000
χ424-440-42i2−2i21-2-1203i−3iζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ232i2−2i21-2-1203i−3i00i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23i2i2−i2−i20000000−i3i30003−300ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ434-440-42i2−2i21-2-1203i−3iζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ232i2−2i21-2-1203i−3i00i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23i2i2−i2−i20000000i3−i3000−3300−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ444-440-42i2−2i21-2-120−3i3i−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232i2−2i21-2-120−3i3i00i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23i2i2−i2−i20000000−i3i3000−3300−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ454-440-42i2−2i21-2-120−3i3i−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232i2−2i21-2-120−3i3i00i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23i2i2−i2−i20000000i3−i30003−300ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ464-440-42i2−2i244-4-4000−2i22i22i2−2i22i2−2i244-4-400000−2i22i2−2i22i22i2−2i2−2i2−2i22i22i2000000000000000000000000000000
χ474-4-202−2i22i244-4-40002i2−2i2−2i22i2i2−i2-2-222000002i2−2i2−i2i2i2−i2−i2−i2i2i20023−230000000000i6−i600000000000000
χ484-4-202−2i22i244-4-40002i2−2i2−2i22i2i2−i2-2-222000002i2−2i2−i2i2i2−i2−i2−i2i2i200−23230000000000−i6i600000000000000
χ494-4-2022i2−2i244-4-4000−2i22i22i2−2i2−i2i2-2-22200000−2i22i2i2−i2−i2i2i2i2−i2−i20023−230000000000−i6i600000000000000
χ504-4-2022i2−2i244-4-4000−2i22i22i2−2i2−i2i2-2-22200000−2i22i2i2−i2−i2i2i2i2−i2−i200−23230000000000i6−i600000000000000
χ51888-8800-42-42-844000000-42-42-244-2-20000000000000000000000000000000000000000
χ5288-48-4882-42-4-4222222-4-4-12-12-4-1-122-4-4-1-1-1-12222000000000000000000000000000000
χ5388-48-488-42-42-4-4-4-4-4-4-4-4-42-12-1222-1-1222222-1-1-1-1000000000000000000000000000000
χ5488-48-4-8-82-42-4-422-2-2-2-244-12-12-4-1-122441111-2-2-2-2000000000000000000000000000000
χ5588-48-4-8-8-42-42-4-4-44444442-12-1222-1-1-2-2-2-2-2-21111000000000000000000000000000000
χ5688-4-8-4002-42-44-2-26i6i−6i−6i00-12-12411-2-200−3i−3i3i3i0000000000000000000000000000000000
χ5788-4-8-4002-42-44-2-2−6i−6i6i6i00-12-12411-2-2003i3i−3i−3i0000000000000000000000000000000000
χ5888-4-8-400-42-424440000002-12-1-2-2-21100000033−3333−33000000000000000000000000000000
χ5988-4-8-400-42-424440000002-12-1-2-2-211000000−3333−3333000000000000000000000000000000
χ608-880-8−4i24i2-424-2000−2i22i22i2−2i2−4i24i2-424-200000i2−i2−2i22i22i2−2i2i2i2−i2−i2000000000000000000000000000000
χ618-880-84i2−4i2-424-20002i2−2i2−2i22i24i2−4i2-424-200000−i2i22i2−2i2−2i22i2−i2−i2i2i2000000000000000000000000000000
χ628-8-404−4i24i22-4-2406i−6i−2ζ5+4ζ7−2ζ13+4ζ232ζ5−4ζ7+2ζ13−4ζ23−4ζ5+2ζ7−4ζ13+2ζ234ζ5−2ζ7+4ζ13−2ζ232i2−2i2-121-20−3i3i00−2i22i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23i2i2−i2−i2000000000000000000000000000000
χ638-8-404−4i24i22-4-240−6i6i4ζ5−2ζ7+4ζ13−2ζ23−4ζ5+2ζ7−4ζ13+2ζ232ζ5−4ζ7+2ζ13−4ζ23−2ζ5+4ζ7−2ζ13+4ζ232i2−2i2-121-203i−3i00−2i22i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23i2i2−i2−i2000000000000000000000000000000
χ648-8-404−4i24i2-424-2000−2i22i22i2−2i22i2−2i22-1-2100033−33i2−i2i2−i2−i2i2ζ5+ζ7−2ζ13−2ζ23−2ζ5−2ζ7+ζ13+ζ23−ζ5−ζ7+2ζ13+2ζ232ζ5+2ζ7−ζ13−ζ23000000000000000000000000000000
χ658-8-404−4i24i2-424-2000−2i22i22i2−2i22i2−2i22-1-21000−3333i2−i2i2−i2−i2i2−2ζ5−2ζ7+ζ13+ζ23ζ5+ζ7−2ζ13−2ζ232ζ5+2ζ7−ζ13−ζ23−ζ5−ζ7+2ζ13+2ζ23000000000000000000000000000000
χ668-8-4044i2−4i22-4-2406i−6i2ζ5−4ζ7+2ζ13−4ζ23−2ζ5+4ζ7−2ζ13+4ζ234ζ5−2ζ7+4ζ13−2ζ23−4ζ5+2ζ7−4ζ13+2ζ23−2i22i2-121-20−3i3i002i2−2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−i2−i2i2i2000000000000000000000000000000
χ678-8-4044i2−4i22-4-240−6i6i−4ζ5+2ζ7−4ζ13+2ζ234ζ5−2ζ7+4ζ13−2ζ23−2ζ5+4ζ7−2ζ13+4ζ232ζ5−4ζ7+2ζ13−4ζ23−2i22i2-121-203i−3i002i2−2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−i2−i2i2i2000000000000000000000000000000
χ688-8-4044i2−4i2-424-20002i2−2i2−2i22i2−2i22i22-1-2100033−33−i2i2−i2i2i2−i2−ζ5−ζ7+2ζ13+2ζ232ζ5+2ζ7−ζ13−ζ23ζ5+ζ7−2ζ13−2ζ23−2ζ5−2ζ7+ζ13+ζ23000000000000000000000000000000
χ698-8-4044i2−4i2-424-20002i2−2i2−2i22i2−2i22i22-1-21000−3333−i2i2−i2i2i2−i22ζ5+2ζ7−ζ13−ζ23−ζ5−ζ7+2ζ13+2ζ23−2ζ5−2ζ7+ζ13+ζ23ζ5+ζ7−2ζ13−2ζ23000000000000000000000000000000

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