Finite Group Databasebeta

← Group #13048747

Character table — Group #13048747

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112222222222222222266669912121212121212121212121212121212121212121212181818181818181818181818181818181854545454108108108108
order123333466661212121212121212336644333336666612121212121212121212121226666666612121212121212122244661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-11-11-1
χ6111111-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-11-11
χ7111111-11111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-111-1-11
χ8111111-11111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1-111-1
χ922222222222222222222-1-12002-1-1-1-12-1-1-1-1-1222-1-1-1-1-1-1-1-1000000000000000002200-1-100
χ1022222222222222222222-1-12002-1-1-1-12-1-1-1-1-1222-1-1-1-1-1-1-1-100000000000000000-2-2001100
χ112222222222222222222-122-100-12-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-100000000000000000002200-1-1
χ122222222222222222222-122-100-12-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-10000000000000000000-2-20011
χ13222222-22222-2-2-2-2-2-2-2-22-1-12002-1-1-1-12-1-1-1-11-2-2-211111111000000000000000002-200-1100
χ14222222-22222-2-2-2-2-2-2-2-22-1-12002-1-1-1-12-1-1-1-11-2-2-21111111100000000000000000-22001-100
χ15222222-22222-2-2-2-2-2-2-2-2-122-100-12-1-1-1-12-1-1-1-2111-2-211111100000000000000000002-200-11
χ16222222-22222-2-2-2-2-2-2-2-2-122-100-12-1-1-1-12-1-1-1-2111-2-21111110000000000000000000-22001-1
χ17222-1-1-122-1-1-122-1-1-1-1-1-1222222-1-12-1-1-1-12-1-122-1-1-1-122-1-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-100000000
χ18222-1-1-122-1-1-122-1-1-1-1-1-12222-2-2-1-12-1-1-1-12-1-122-1-1-1-122-1-1-1-1-2-2-2111111-2-211111100000000
χ19222-1-1-1-22-1-1-1-2-2111111222222-1-12-1-1-1-12-1-1-2-21111-2-21111-2-2-211111122-1-1-1-1-1-100000000
χ20222-1-1-1-22-1-1-1-2-21111112222-2-2-1-12-1-1-1-12-1-1-2-21111-2-21111222-1-1-1-1-1-1-2-211111100000000
χ212-222220-2-2-2-20000000022-2-22i−2i22222-2-2-2-2-20000000000000000000002i−2i2i2i2i−2i−2i−2i00000000
χ222-222220-2-2-2-20000000022-2-2−2i2i22222-2-2-2-2-2000000000000000000000−2i2i−2i−2i−2i2i2i2i00000000
χ232-22-1-1-10-211100333−3−3−322-2-22i−2i-1-12-1-111-211003−33−30033−3−3000−i3−i3−i3i3i3i32i−2i−i−i−iiii00000000
χ242-22-1-1-10-211100333−3−3−322-2-2−2i2i-1-12-1-111-211003−33−30033−3−3000i3i3i3−i3−i3−i3−2i2iiii−i−i−i00000000
χ252-22-1-1-10-211100−3−3−333322-2-22i−2i-1-12-1-111-21100−33−3300−3−333000i3i3i3−i3−i3−i32i−2i−i−i−iiii00000000
χ262-22-1-1-10-211100−3−3−333322-2-2−2i2i-1-12-1-111-21100−33−3300−3−333000−i3−i3−i3i3i3i3−2i2iiii−i−i−i00000000
χ274444444444444444444-2-2-2-200-2-2111-2-2111-2-2-2-2-2-21111110000000000000000000000000
χ28444444-44444-4-4-4-4-4-4-4-4-2-2-2-200-2-2111-2-2111222222-1-1-1-1-1-10000000000000000000000000
χ29444-2-2-244-2-2-244-2-2-2-2-2-24-2-2400-21-211-21-211-24-2-211-2-211110000000000000000000000000
χ30444-2-2-244-2-2-244-2-2-2-2-2-2-244-2001-2-2111-2-2114-211-2-2-2-211110000000000000000000000000
χ31444-2-2-244-2-2-244-2-2-2-2-2-2-2-2-2-200111−1−3i32−1+3i32111−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i320000000000000000000000000
χ32444-2-2-244-2-2-244-2-2-2-2-2-2-2-2-2-200111−1+3i32−1−3i32111−1+3i32−1−3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i320000000000000000000000000
χ33444-2-2-2-44-2-2-2-4-42222224-2-2400-21-211-21-2112-422-1-122-1-1-1-10000000000000000000000000
χ34444-2-2-2-44-2-2-2-4-4222222-244-2001-2-2111-2-211-42-1-12222-1-1-1-10000000000000000000000000
χ35444-2-2-2-44-2-2-2-4-4222222-2-2-2-200111−1−3i32−1+3i32111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321−3i321+3i321−3i320000000000000000000000000
χ36444-2-2-2-44-2-2-2-4-4222222-2-2-2-200111−1+3i32−1−3i32111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321+3i321−3i321+3i320000000000000000000000000
χ374-444440-4-4-4-4000000004-22-4004-2-2-2-2-422220000000000000000000000000000000000000
χ384-444440-4-4-4-400000000-24-4200-24-2-2-22-42220000000000000000000000000000000000000
χ394-444440-4-4-4-400000000-2-22200-2-211122-1-1-10000003i−3i3i−3i−3i3i0000000000000000000000000
χ404-444440-4-4-4-400000000-2-22200-2-211122-1-1-1000000−3i3i−3i3i3i−3i0000000000000000000000000
χ414-44-2-2-20-422200232323−23−23−234-22-400-21-2112-12-1-10023−23−3300−3−3330000000000000000000000000
χ424-44-2-2-20-422200232323−23−23−23-24-42001-2-211-122-1-100−3323−2300−3−3330000000000000000000000000
χ434-44-2-2-20-422200232323−23−23−23-2-22200111−1−3i32−1+3i32-1-1-11+3i321−3i3200−33−333i−3iζ7+2ζ11−2ζ7−ζ11−ζ7−2ζ112ζ7+ζ110000000000000000000000000
χ444-44-2-2-20-422200232323−23−23−23-2-22200111−1+3i32−1−3i32-1-1-11−3i321+3i3200−33−33−3i3i−2ζ7−ζ11ζ7+2ζ112ζ7+ζ11−ζ7−2ζ110000000000000000000000000
χ454-44-2-2-20-422200−23−23−232323234-22-400-21-2112-12-1-100−23233−30033−3−30000000000000000000000000
χ464-44-2-2-20-422200−23−23−23232323-24-42001-2-211-122-1-1003−3−23230033−3−30000000000000000000000000
χ474-44-2-2-20-422200−23−23−23232323-2-22200111−1−3i32−1+3i32-1-1-11+3i321−3i32003−33−3−3i3i−ζ7−2ζ112ζ7+ζ11ζ7+2ζ11−2ζ7−ζ110000000000000000000000000
χ484-44-2-2-20-422200−23−23−23232323-2-22200111−1+3i32−1−3i32-1-1-11−3i321+3i32003−33−33i−3i2ζ7+ζ11−ζ7−2ζ11−2ζ7−ζ11ζ7+2ζ110000000000000000000000000
χ4966-36-3-36-36-3-3-3-36-3-36-3-300002200000000000000000000002-1-12-1-12-1-1-1-12-1-12-1-100000000
χ5066-36-3-36-36-3-3-3-36-3-36-3-30000-2-20000000000000000000000-211-211-21111-211-21100000000
χ5166-36-3-3-6-36-3-333-633-6330000220000000000000000000000-211-211-211-1-12-1-12-1-100000000
χ5266-36-3-3-6-36-3-333-633-6330000-2-200000000000000000000002-1-12-1-12-1-111-211-21100000000
χ5366-3-36-36-3-36-3-3-3-36-3-36-300002200000000000000000000002-1-1-12-1-12-1-1-1-12-1-12-100000000
χ5466-3-36-36-3-36-3-3-3-36-3-36-30000-2-20000000000000000000000-2111-211-21111-211-2100000000
χ5566-3-36-3-6-3-36-3333-633-630000220000000000000000000000-2111-211-21-1-1-12-1-12-100000000
χ5666-3-36-3-6-3-36-3333-633-630000-2-200000000000000000000002-1-1-12-1-12-1111-211-2100000000
χ5766-3-3-366-3-3-36-3-3-3-36-3-3600002200000000000000000000002-1-1-1-12-1-12-1-1-1-12-1-1200000000
χ5866-3-3-366-3-3-36-3-3-3-36-3-360000-2-20000000000000000000000-21111-211-21111-211-200000000
χ5966-3-3-36-6-3-3-363333-633-60000220000000000000000000000-21111-211-2-1-1-1-12-1-1200000000
χ6066-3-3-36-6-3-3-363333-633-60000-2-200000000000000000000002-1-1-1-12-1-121111-211-200000000
χ616-6-36-3-303-63333−33033−330−333300002i−2i00000000000000000000000−i3i30−i3i30i3−i3−ii2i−i−i−2iii00000000
χ626-6-36-3-303-63333−33033−330−33330000−2i2i00000000000000000000000i3−i30i3−i30−i3i3i−i−2iii2i−i−i00000000
χ636-6-36-3-303-633−33330−3333033−3300002i−2i00000000000000000000000i3−i30i3−i30−i3i3−ii2i−i−i−2iii00000000
χ646-6-36-3-303-633−33330−3333033−330000−2i2i00000000000000000000000−i3i30−i3i30i3−i3i−i−2iii2i−i−i00000000
χ656-6-3-36-3033-6333−33−33033330−3300002i−2i00000000000000000000000−i3i3i30−i3−i30i3−ii−i2i−ii−2ii00000000
χ666-6-3-36-3033-6333−33−33033330−330000−2i2i00000000000000000000000i3−i3−i30i3i30−i3i−ii−2ii−i2i−i00000000
χ676-6-3-36-3033-63−3333330−33−3303300002i−2i00000000000000000000000i3−i3−i30i3i30−i3−ii−i2i−ii−2ii00000000
χ686-6-3-36-3033-63−3333330−33−330330000−2i2i00000000000000000000000−i3i3i30−i3−i30i3i−ii−2ii−i2i−i00000000
χ696-6-3-3-360333-633−3333−330−3333000002i−2i00000000000000000000000−i3i3−i3i30i3−i30−ii−i−i2iii−2i00000000
χ706-6-3-3-360333-633−3333−330−333300000−2i2i00000000000000000000000i3−i3i3−i30−i3i30i−iii−2i−i−i2i00000000
χ716-6-3-3-360333-6−3333−3333033−33000002i−2i00000000000000000000000i3−i3i3−i30−i3i30−ii−i−i2iii−2i00000000
χ726-6-3-3-360333-6−3333−3333033−3300000−2i2i00000000000000000000000−i3i3−i3i30i3−i30i−iii−2i−i−i2i00000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.