Finite Group Databasebeta

← Group #13166393

Character table — Group #13166393

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222224444444444888888888888888888889912121818181818181824242424242424243636363636363636363636363636108108108108108108
order122344612123366612121212123366666666121212121212121212122288244661212242424242424242444446121212121212121212444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111
χ311111111111111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ5111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-111111111i−ii−i-1-1iiii−i−i−i−iii−i−i-1-1
χ6111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-111111111−ii−ii-1-1−i−i−i−iiiii−i−iii-1-1
χ7111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−i-1-1iiii−i−i−i−i−i−iii11
χ8111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii-1-1−i−i−i−iiiiiii−i−i11
χ911-11-111-1-111-1111111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-11-111-1-11111-1-1-1-111-1-1-1111-1-111-1-11-11-11-1
χ1011-11-111-1-111-1111111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-11-111-1-11111-1-1-1-1-1-111-11-1-111-1-111-11-111-1
χ1111-11-111-1-111-1111111111-1-1-1-1-1-111-1-11111-1-1-1-111-11-11-111-1-1-1-1-1-1111111-1-1-1111-1-111-1-1-11-11-11
χ1211-11-111-1-111-1111111111-1-1-1-1-1-111-1-11111-1-1-1-111-11-11-111-1-1-1-1-1-11111-1-111-11-1-111-1-1111-11-1-11
χ1311-11-111-1-111-1111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-11-11-1-1111111-1-1-1-1i−i−ii1-1ii−i−i−i−iiii−i−ii-11
χ1411-11-111-1-111-1111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-11-11-1-1111111-1-1-1-1−iii−i1-1−i−iiiii−i−i−iii−i-11
χ1511-11-111-1-111-1111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-111-11-1-111-1-1-1-11111i−i−ii1-1ii−i−i−i−iii−iii−i1-1
χ1611-11-111-1-111-1111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-111-11-1-111-1-1-1-11111−iii−i1-1−i−iiiii−i−ii−i−ii1-1
χ172222-2-22-2-222222-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-222002-2-222-2-20000000000002-200000000000000
χ182222-2-22-2-222222-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-200-222-2-222000000000000-2200000000000000
χ19222-122-1-1-122-122-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-12200222-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1000000
χ20222-122-1-1-122-122-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-12200222-1-1-1-100000000-2-2-2-2-1-111111111000000
χ21222-122-1-1-122-122-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-200-2-2-21111000000002i−2i2i−2i11−i−i−i−iiiii000000
χ22222-122-1-1-122-122-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-200-2-2-2111100000000−2i2i−2i2i11iiii−i−i−i−i000000
χ23222-1-2-2-11122-1221-2-2-2-2-1-122-1-1-1-1-1-1-2-21111111122002-2-2-1-111000000000000-11−i3i3−i3i3−i3i3−i3i3000000
χ24222-1-2-2-11122-1221-2-2-2-2-1-122-1-1-1-1-1-1-2-21111111122002-2-2-1-111000000000000-11i3−i3i3−i3i3−i3i3−i3000000
χ25222-1-2-2-11122-1221-2-2-2-2-1-122-1-1-1-1-1-1-2-211111111-2-200-22211-1-10000000000001-13−33−3−33−33000000
χ26222-1-2-2-11122-1221-2-2-2-2-1-122-1-1-1-1-1-1-2-211111111-2-200-22211-1-10000000000001-1−33−333−33−3000000
χ2722-222-222222-222-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-222222200-2-222222000000000000-2-200000000000000
χ2822-222-222222-222-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-22222-2-20022-2-2-2-2-20000000000002200000000000000
χ2922-2-12-2-1-1-1221221-2-2-2-2-1-1-2-21111-1-1221111-1-1-1-12200-2-22-1-1-1-100000000000011−i3i3i3−i3−i3i3i3−i3000000
χ3022-2-12-2-1-1-1221221-2-2-2-2-1-1-2-21111-1-1221111-1-1-1-12200-2-22-1-1-1-100000000000011i3−i3−i3i3i3−i3−i3i3000000
χ3122-2-12-2-1-1-1221221-2-2-2-2-1-1-2-21111-1-1221111-1-1-1-1-2-20022-21111000000000000-1-13−3−33−333−3000000
χ3222-2-12-2-1-1-1221221-2-2-2-2-1-1-2-21111-1-1221111-1-1-1-1-2-20022-21111000000000000-1-1−333−33−3−33000000
χ3322-2-1-22-11122122-12222-1-1-2-21111-1-1-2-2-1-1-1-111112200-22-2-1-1110000000022-2-21-1-1-111-1-111000000
χ3422-2-1-22-11122122-12222-1-1-2-21111-1-1-2-2-1-1-1-111112200-22-2-1-11100000000-2-2221-111-1-111-1-1000000
χ3522-2-1-22-11122122-12222-1-1-2-21111-1-1-2-2-1-1-1-11111-2-2002-2211-1-1000000002i−2i−2i2i-11−i−iiiii−i−i000000
χ3622-2-1-22-11122122-12222-1-1-2-21111-1-1-2-2-1-1-1-11111-2-2002-2211-1-100000000−2i2i2i−2i-11ii−i−i−i−iii000000
χ374444444441-241-2411-2-21-21-211-2-21-21-211-2-211-2-20044000000011-2-211-2-200000000000000000000
χ384444444441-241-2411-2-21-21-211-2-21-21-211-2-211-2-200-4-40000000-1-122-1-12200000000000000000000
χ39444444444-214-214-2-211-21-21-2-211-21-21-2-211-2-21100440000000-2-211-2-21100000000000000000000
χ40444444444-214-214-2-211-21-21-2-211-21-21-2-211-2-21100-4-4000000022-1-122-1-100000000000000000000
χ414444-4-44-4-41-241-2-4-1-1221-21-211-2-21-2-12-1-122-1-122000000000003i−3i003i−3i0000000000000000000000
χ424444-4-44-4-41-241-2-4-1-1221-21-211-2-21-2-12-1-122-1-12200000000000−3i3i00−3i3i0000000000000000000000
χ434444-4-44-4-4-214-21-422-1-1-21-21-2-211-212-122-1-122-1-100000000000003i−3i003i−3i00000000000000000000
χ444444-4-44-4-4-214-21-422-1-1-21-21-2-211-212-122-1-122-1-10000000000000−3i3i00−3i3i00000000000000000000
χ4544-444-44441-2-41-2-4-1-1221-2-12-1-1221-21-2-1-12211-2-2000000000003i−3i00−3i3i0000000000000000000000
χ4644-444-44441-2-41-2-4-1-1221-2-12-1-1221-21-2-1-12211-2-200000000000−3i3i003i−3i0000000000000000000000
χ4744-444-4444-21-4-21-422-1-1-212-122-1-1-21-2122-1-1-2-21100000000000003i−3i00−3i3i00000000000000000000
χ4844-444-4444-21-4-21-422-1-1-212-122-1-1-21-2122-1-1-2-2110000000000000−3i3i003i−3i00000000000000000000
χ4944-44-444-4-41-2-41-2411-2-21-2-12-1-1221-2-1211-2-2-1-122004-4000000011-2-2-1-12200000000000000000000
χ5044-44-444-4-41-2-41-2411-2-21-2-12-1-1221-2-1211-2-2-1-12200-440000000-1-12211-2-200000000000000000000
χ5144-44-444-4-4-21-4-214-2-211-212-122-1-1-212-1-2-21122-1-1004-40000000-2-21122-1-100000000000000000000
χ5244-44-444-4-4-21-4-214-2-211-212-122-1-1-212-1-2-21122-1-100-44000000022-1-1-2-21100000000000000000000
χ534-40400-400440-4-40000044000000-4-400000000004-4000004-4000000000000000000000000000000
χ544-40400-400440-4-40000044000000-4-40000000000-4400000-44000000000000000000000000000000
χ554-40-200223−23440-4-400000-2-20000002200000023−2323−234-400000-2223−230000000000000000000000000000
χ564-40-200223−23440-4-400000-2-20000002200000023−2323−23-44000002-2−23230000000000000000000000000000
χ574-40-2002−2323440-4-400000-2-200000022000000−2323−23234-400000-22−23230000000000000000000000000000
χ584-40-2002−2323440-4-400000-2-200000022000000−2323−2323-44000002-223−230000000000000000000000000000
χ59888-488-4-4-42-4-42-4-422-4-4-122-4-1-122-122-4-1-122-1-122000000000000000000000000000000000000000
χ60888-488-4-4-4-42-4-42-4-4-4222-1-4222-1-12-1-4222-1-122-1-1000000000000000000000000000000000000000
χ61888-4-8-8-4442-4-42-44-2-244-122-4-1-122-12-2411-2-211-2-2000000000000000000000000000000000000000
χ62888-4-8-8-444-42-4-42444-2-22-1-4222-1-12-14-2-2-211-2-211000000000000000000000000000000000000000
χ6388-8-48-8-4-4-42-442-44-2-244-12-2411-2-2-122-411-2-2-1-122000000000000000000000000000000000000000
χ6488-8-48-8-4-4-4-424-42444-2-22-14-2-2-2112-1-42-2-21122-1-1000000000000000000000000000000000000000
χ6588-8-4-88-4442-442-4-422-4-4-12-2411-2-2-12-24-1-12211-2-2000000000000000000000000000000000000000
χ6688-8-4-88-444-424-42-4-4-4222-14-2-2-2112-14-222-1-1-2-211000000000000000000000000000000000000000
χ678-80800-8002-40-2406i−6i002-4000000-24006i−6i000000000000000000000000000000000000000000000
χ688-80800-8002-40-240−6i6i002-4000000-2400−6i6i000000000000000000000000000000000000000000000
χ698-80800-800-4204-20006i−6i-420000004-200006i−6i0000000000000000000000000000000000000000000
χ708-80800-800-4204-2000−6i6i-420000004-20000−6i6i0000000000000000000000000000000000000000000
χ718-80-400443−432-40-2406i−6i00-1200−3i33i3001-200−3i3i003−3−2323000000000000000000000000000000000000000
χ728-80-400443−432-40-240−6i6i00-12003i3−3i3001-2003i−3i003−3−2323000000000000000000000000000000000000000
χ738-80-400443−43-4204-20006i−6i2-10000−3i33i3-210000−3i3i−23233−3000000000000000000000000000000000000000
χ748-80-400443−43-4204-2000−6i6i2-100003i3−3i3-2100003i−3i−23233−3000000000000000000000000000000000000000
χ758-80-4004−43432-40-2406i−6i00-12003i3−3i3001-200−3i3i00−3323−23000000000000000000000000000000000000000
χ768-80-4004−43432-40-240−6i6i00-1200−3i33i3001-2003i−3i00−3323−23000000000000000000000000000000000000000
χ778-80-4004−4343-4204-20006i−6i2-100003i3−3i3-210000−3i3i23−23−33000000000000000000000000000000000000000
χ788-80-4004−4343-4204-2000−6i6i2-10000−3i33i3-2100003i−3i23−23−33000000000000000000000000000000000000000

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