Finite Group Databasebeta

← Group #13166375

Character table — Group #13166375

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222224444444444888888888888888888889912121818181818181824242424242424243636363636363636363636363636108108108108108108
order12234461212336666666123366666612121212121212121212121244222246612126666666644446121212121212121212448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-111111111ii−i−i-1-1iiii−i−i−i−i-1-1ii−i−i
χ6111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-111111111−i−iii-1-1−i−i−i−iiiii-1-1−i−iii
χ7111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i11−i−iii
χ8111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii11ii−i−i
χ911-111-111111-1-1-1-1-111-111-1-1-1-11111-1-11111-1-1-1-1111-1-11-111111111-1-1-1-11-11-1-1-111-1-111-1-11-11-11-1
χ1011-111-111111-1-1-1-1-111-111-1-1-1-11111-1-11111-1-1-1-1111-1-11-111111111-1-1-1-1-11-11-1-1-1-111-1-1111-1-11-11
χ1111-111-111111-1-1-1-1-111-111-1-1-1-11111-1-11111-1-1-1-111-11-11-11111-1-1-1-111111-11-1-1-111-1-111-1-1-11-11-11
χ1211-111-111111-1-1-1-1-111-111-1-1-1-11111-1-11111-1-1-1-111-11-11-11111-1-1-1-11111-11-11-1-1-1-111-1-111-111-11-1
χ1311-111-111111-1-1-1-1-111-111-1-1-1-11111-1-11111-1-1-1-1-1-11-11-11-1-1-1-11111-1-1-1-1i−i−ii11ii−i−i−i−iii-11i−i−ii
χ1411-111-111111-1-1-1-1-111-111-1-1-1-11111-1-11111-1-1-1-1-1-11-11-11-1-1-1-11111-1-1-1-1−iii−i11−i−iiiii−i−i-11−iii−i
χ1511-111-111111-1-1-1-1-111-111-1-1-1-11111-1-11111-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-11111i−i−ii11ii−i−i−i−iii1-1−iii−i
χ1611-111-111111-1-1-1-1-111-111-1-1-1-11111-1-11111-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-11111−iii−i11−i−iiiii−i−i1-1i−i−ii
χ172222-2-22-2-2222222222-222222222-2-2-2-2-2-2-2-2-2-2-2-22200-2-22-2-222000000000000-2200000000000000
χ182222-2-22-2-2222222222-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20022-222-2-20000000000002-200000000000000
χ19222-122-1-1-122-1222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200222-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1000000
χ20222-122-1-1-122-1222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200222-1-1-1-100000000-2-2-2-2-1-111111111000000
χ21222-122-1-1-122-1222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-200-2-2-21111000000002i2i−2i−2i11−i−i−i−iiiii000000
χ22222-122-1-1-122-1222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-200-2-2-2111100000000−2i−2i2i2i11iiii−i−i−i−i000000
χ23222-1-2-2-11122-12222221-1-1-1-1-1-1-1-1-2-2-2-2111111112200-2-2211-1-10000000000001-13−33−33−33−3000000
χ24222-1-2-2-11122-12222221-1-1-1-1-1-1-1-1-2-2-2-2111111112200-2-2211-1-10000000000001-1−33−33−33−33000000
χ25222-1-2-2-11122-12222221-1-1-1-1-1-1-1-1-2-2-2-211111111-2-20022-2-1-111000000000000-11−i3i3−i3i3i3−i3i3−i3000000
χ26222-1-2-2-11122-12222221-1-1-1-1-1-1-1-1-2-2-2-211111111-2-20022-2-1-111000000000000-11i3−i3i3−i3−i3i3−i3i3000000
χ2722-22-222-2-222-2-2-2-2-222222-2-2-2-222-2-222-2-2-2-2222222002-2-2-2-2220000000000002-200000000000000
χ2822-22-222-2-222-2-2-2-2-222222-2-2-2-222-2-222-2-2-2-22222-2-200-22222-2-2000000000000-2200000000000000
χ2922-2-12-2-1-1-1221-2-2-2-2221-1-11111-1-122-2-2-1-1-1-111112200-22-2-1-1-1-1000000002-22-211-1-111-1-111000000
χ3022-2-12-2-1-1-1221-2-2-2-2221-1-11111-1-122-2-2-1-1-1-111112200-22-2-1-1-1-100000000-22-221111-1-111-1-1000000
χ3122-2-12-2-1-1-1221-2-2-2-2221-1-11111-1-122-2-2-1-1-1-11111-2-2002-221111000000002i−2i−2i2i-1-1−i−iiiii−i−i000000
χ3222-2-12-2-1-1-1221-2-2-2-2221-1-11111-1-122-2-2-1-1-1-11111-2-2002-22111100000000−2i2i2i−2i-1-1ii−i−i−i−iii000000
χ3322-2-1-22-111221-2-2-2-222-1-1-11111-1-1-2-2221111-1-1-1-122002-2-211-1-1000000000000-113−3−333−3−33000000
χ3422-2-1-22-111221-2-2-2-222-1-1-11111-1-1-2-2221111-1-1-1-122002-2-211-1-1000000000000-11−333−3−333−3000000
χ3522-2-1-22-111221-2-2-2-222-1-1-11111-1-1-2-2221111-1-1-1-1-2-200-222-1-1110000000000001-1−i3i3i3−i3i3−i3−i3i3000000
χ3622-2-1-22-111221-2-2-2-222-1-1-11111-1-1-2-2221111-1-1-1-1-2-200-222-1-1110000000000001-1i3−i3−i3i3−i3i3i3−i3000000
χ374444444441-2411-2-21-241-211-2-21-21-21-211-2-211-2-20044000000011-2-211-2-200000000000000000000
χ384444444441-2411-2-21-241-211-2-21-21-21-211-2-211-2-200-4-40000000-1-122-1-12200000000000000000000
χ39444444444-214-2-211-214-21-2-211-21-21-21-2-211-2-21100440000000-2-211-2-21100000000000000000000
χ40444444444-214-2-211-214-21-2-211-21-21-21-2-211-2-21100-4-4000000022-1-122-1-100000000000000000000
χ414444-4-44-4-41-2411-2-21-2-41-211-2-21-2-12-12-1-122-1-122000000000003-3003-30000000000000000000000
χ424444-4-44-4-41-2411-2-21-2-41-211-2-21-2-12-12-1-122-1-12200000000000-3300-330000000000000000000000
χ434444-4-44-4-4-214-2-211-21-4-21-2-211-212-12-122-1-122-1-100000000000003-3003-300000000000000000000
χ444444-4-44-4-4-214-2-211-21-4-21-2-211-212-12-122-1-122-1-10000000000000-3300-3300000000000000000000
χ4544-444-44441-2-4-1-1221-2-41-2-1-1221-21-2-1211-2-2-1-122004-4000000011-2-2-1-12200000000000000000000
χ4644-444-44441-2-4-1-1221-2-41-2-1-1221-21-2-1211-2-2-1-12200-440000000-1-12211-2-200000000000000000000
χ4744-444-4444-21-422-1-1-21-4-2122-1-1-21-212-1-2-21122-1-1004-40000000-2-21122-1-100000000000000000000
χ4844-444-4444-21-422-1-1-21-4-2122-1-1-21-212-1-2-21122-1-100-44000000022-1-1-2-21100000000000000000000
χ4944-44-444-4-41-2-4-1-1221-241-2-1-1221-2-121-2-1-12211-2-2000000000003-300-330000000000000000000000
χ5044-44-444-4-41-2-4-1-1221-241-2-1-1221-2-121-2-1-12211-2-200000000000-33003-30000000000000000000000
χ5144-44-444-4-4-21-422-1-1-214-2122-1-1-212-1-2122-1-1-2-21100000000000003-300-3300000000000000000000
χ5244-44-444-4-4-21-422-1-1-214-2122-1-1-212-1-2122-1-1-2-2110000000000000-33003-300000000000000000000
χ534-40400-4004400000-4-40440000-4-40000000000004i−4i00000004i−4i0000000000000000000000000000
χ544-40400-4004400000-4-40440000-4-4000000000000−4i4i0000000−4i4i0000000000000000000000000000
χ554-40-200223−234400000-4-40-2-2000022000023−2323−2300004i−4i00000−2i32i3−2i2i0000000000000000000000000000
χ564-40-200223−234400000-4-40-2-2000022000023−2323−230000−4i4i000002i3−2i32i−2i0000000000000000000000000000
χ574-40-2002−23234400000-4-40-2-20000220000−2323−232300004i−4i000002i3−2i3−2i2i0000000000000000000000000000
χ584-40-2002−23234400000-4-40-2-20000220000−2323−23230000−4i4i00000−2i32i32i−2i0000000000000000000000000000
χ59888-488-4-4-42-4-422-4-42-4-4-12-1-122-122-42-4-1-122-1-122000000000000000000000000000000000000000
χ60888-488-4-4-4-42-4-4-422-42-42-122-1-12-1-42-4222-1-122-1-1000000000000000000000000000000000000000
χ61888-4-8-8-4442-4-422-4-42-44-12-1-122-12-24-2411-2-211-2-2000000000000000000000000000000000000000
χ62888-4-8-8-444-42-4-4-422-4242-122-1-12-14-24-2-2-211-2-211000000000000000000000000000000000000000
χ6388-8-48-8-4-4-42-44-2-2442-44-1211-2-2-122-4-24-1-12211-2-2000000000000000000000000000000000000000
χ6488-8-48-8-4-4-4-42444-2-2-4242-1-2-2112-1-424-222-1-1-2-211000000000000000000000000000000000000000
χ6588-8-4-88-4442-44-2-2442-4-4-1211-2-2-12-242-411-2-2-1-122000000000000000000000000000000000000000
χ6688-8-4-88-444-42444-2-2-42-42-1-2-2112-14-2-42-2-21122-1-1000000000000000000000000000000000000000
χ678-80800-8002-406-600-2402-46-600-24000000000000000000000000000000000000000000000000000
χ688-80800-8002-40-6600-2402-4-6600-24000000000000000000000000000000000000000000000000000
χ698-80800-800-420006-64-20-42006-64-2000000000000000000000000000000000000000000000000000
χ708-80800-800-42000-664-20-4200-664-2000000000000000000000000000000000000000000000000000
χ718-80-400443−432-406-600-240-12-33001-200003−3−232333−3300000000000000000000000000000000000000000
χ728-80-400443−432-40-6600-240-123-3001-200003−3−2323−333300000000000000000000000000000000000000000
χ738-80-400443−43-420006-64-202-100-33-210000−23233−30033−33000000000000000000000000000000000000000
χ748-80-400443−43-42000-664-202-1003-3-210000−23233−300−3333000000000000000000000000000000000000000
χ758-80-4004−43432-406-600-240-12-33001-20000−3323−23−333300000000000000000000000000000000000000000
χ768-80-4004−43432-40-6600-240-123-3001-20000−3323−2333−3300000000000000000000000000000000000000000
χ778-80-4004−4343-420006-64-202-100-33-21000023−23−3300−3333000000000000000000000000000000000000000
χ788-80-4004−4343-42000-664-202-1003-3-21000023−23−330033−33000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).