Finite Group Databasebeta

← Group #13166397

Character table — Group #13166397

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222224444444444888888888888888888889912121818181818181824242424242424243636363636363636363636363636108108108108108108
order122344666336612121212121233666666661212121212121212121244882241212121224242424242424246688882424242424242424888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-111111111-1-1ii−i−iiiii−i−i−i−i-1-1ii−i−i
χ6111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-111111111-1-1−i−iii−i−i−i−iiiii-1-1−i−iii
χ7111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i11−i−iii
χ8111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii11ii−i−i
χ911-11-11-1-1111111-1111111-1-1-1-1-1-111-1-11111-1-1-1-1111-11-1-1-1-1111111-1-1-1-11-11-11-111-1-111-1-11-11-11-1
χ1011-11-11-1-1111111-1111111-1-1-1-1-1-111-1-11111-1-1-1-1111-11-1-1-1-1111111-1-1-1-11-1-11-11-1-111-1-1111-1-11-11
χ1111-11-11-1-1111111-1111111-1-1-1-1-1-111-1-11111-1-1-1-111-111-1-1-1-111-1-1-1-111111-11-11-111-1-111-1-1-11-11-11
χ1211-11-11-1-1111111-1111111-1-1-1-1-1-111-1-11111-1-1-1-111-111-1-1-1-111-1-1-1-111111-1-11-11-1-111-1-111-111-11-1
χ1311-11-11-1-1111111-1111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-1-11111-1-11111-1-1-1-1-11i−i−iiii−i−i−i−iii-11i−i−ii
χ1411-11-11-1-1111111-1111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-1-11111-1-11111-1-1-1-1-11−iii−i−i−iiiii−i−i-11−iii−i
χ1511-11-11-1-1111111-1111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-11-11111-1-1-1-1-1-11111-11i−i−iiii−i−i−i−iii1-1−iii−i
χ1611-11-11-1-1111111-1111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-11-11111-1-1-1-1-1-11111-11−iii−i−i−iiiii−i−i1-1i−i−ii
χ172222-2-22222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-22200-2-22222200000000-2-2000000000000000000
χ182222-2-22222222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-2-2-2-20000000022000000000000000000
χ19222-122-1-1-12222-1-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-12200222-1-1-1-100000000-1-12222-1-1-1-1-1-1-1-1000000
χ20222-122-1-1-12222-1-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-12200222-1-1-1-100000000-1-1-2-2-2-211111111000000
χ21222-122-1-1-12222-1-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-200-2-2-2111100000000112i2i−2i−2i−i−i−i−iiiii000000
χ22222-122-1-1-12222-1-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-200-2-2-211110000000011−2i−2i2i2iiiii−i−i−i−i000000
χ23222-1-2-2-1-1-1222211-2-2-2-2-1-122-1-1-1-1-1-1-2-2111111112200-2-22-1-1-1-100000000110000−i3i3−i3i3−i3i3−i3i3000000
χ24222-1-2-2-1-1-1222211-2-2-2-2-1-122-1-1-1-1-1-1-2-2111111112200-2-22-1-1-1-100000000110000i3−i3i3−i3i3−i3i3−i3000000
χ25222-1-2-2-1-1-1222211-2-2-2-2-1-122-1-1-1-1-1-1-2-211111111-2-20022-2111100000000-1-100003−33−3−33−33000000
χ26222-1-2-2-1-1-1222211-2-2-2-2-1-122-1-1-1-1-1-1-2-211111111-2-20022-2111100000000-1-10000−33−333−33−3000000
χ2722-222-2-2-222222-22-2-2-2-222-2-2-2-2-2-22222-2-2-2-222222200-22-2-2-22200000000-22000000000000000000
χ2822-222-2-2-222222-22-2-2-2-222-2-2-2-2-2-22222-2-2-2-22222-2-2002-2222-2-2000000002-2000000000000000000
χ2922-2-12-211-122221-1-2-2-2-2-1-1-2-21111-1-1221111-1-1-1-12200-22-211-1-1000000001-10000−i3i3i3−i3−i3i3i3−i3000000
χ3022-2-12-211-122221-1-2-2-2-2-1-1-2-21111-1-1221111-1-1-1-12200-22-211-1-1000000001-10000i3−i3−i3i3i3−i3−i3i3000000
χ3122-2-12-211-122221-1-2-2-2-2-1-1-2-21111-1-1221111-1-1-1-1-2-2002-22-1-11100000000-1100003−3−33−333−3000000
χ3222-2-12-211-122221-1-2-2-2-2-1-1-2-21111-1-1221111-1-1-1-1-2-2002-22-1-11100000000-110000−333−33−3−33000000
χ3322-2-1-2211-12222-112222-1-1-2-21111-1-1-2-2-1-1-1-1111122002-2-211-1-100000000-112-22-2-1-111-1-111000000
χ3422-2-1-2211-12222-112222-1-1-2-21111-1-1-2-2-1-1-1-1111122002-2-211-1-100000000-11-22-2211-1-111-1-1000000
χ3522-2-1-2211-12222-112222-1-1-2-21111-1-1-2-2-1-1-1-11111-2-200-222-1-111000000001-12i−2i−2i2i−i−iiiii−i−i000000
χ3622-2-1-2211-12222-112222-1-1-2-21111-1-1-2-2-1-1-1-11111-2-200-222-1-111000000001-1−2i2i2i−2iii−i−i−i−iii000000
χ374444444441-21-24411-2-21-21-211-2-21-21-211-2-211-2-20044000000011-2-211-2-200000000000000000000
χ384444444441-21-24411-2-21-21-211-2-21-21-211-2-211-2-200-4-40000000-1-122-1-12200000000000000000000
χ39444444444-21-2144-2-211-21-21-2-211-21-21-2-211-2-21100440000000-2-211-2-21100000000000000000000
χ40444444444-21-2144-2-211-21-21-2-211-21-21-2-211-2-21100-4-4000000022-1-122-1-100000000000000000000
χ414444-4-44441-21-2-4-4-1-1221-21-211-2-21-2-12-1-122-1-122000000000003i−3i003i−3i0000000000000000000000
χ424444-4-44441-21-2-4-4-1-1221-21-211-2-21-2-12-1-122-1-12200000000000−3i3i00−3i3i0000000000000000000000
χ434444-4-4444-21-21-4-422-1-1-21-21-2-211-212-122-1-122-1-100000000000003i−3i003i−3i00000000000000000000
χ444444-4-4444-21-21-4-422-1-1-21-21-2-211-212-122-1-122-1-10000000000000−3i3i00−3i3i00000000000000000000
χ4544-444-4-4-441-21-2-44-1-1221-2-12-1-1221-21-2-1-12211-2-2000000000003i−3i00−3i3i0000000000000000000000
χ4644-444-4-4-441-21-2-44-1-1221-2-12-1-1221-21-2-1-12211-2-200000000000−3i3i003i−3i0000000000000000000000
χ4744-444-4-4-44-21-21-4422-1-1-212-122-1-1-21-2122-1-1-2-21100000000000003i−3i00−3i3i00000000000000000000
χ4844-444-4-4-44-21-21-4422-1-1-212-122-1-1-21-2122-1-1-2-2110000000000000−3i3i003i−3i00000000000000000000
χ4944-44-44-4-441-21-24-411-2-21-2-12-1-1221-2-1211-2-2-1-122004-4000000011-2-2-1-12200000000000000000000
χ5044-44-44-4-441-21-24-411-2-21-2-12-1-1221-2-1211-2-2-1-12200-440000000-1-12211-2-200000000000000000000
χ5144-44-44-4-44-21-214-4-2-211-212-122-1-1-212-1-2-21122-1-1004-40000000-2-21122-1-100000000000000000000
χ5244-44-44-4-44-21-214-4-2-211-212-122-1-1-212-1-2-21122-1-100-44000000022-1-1-2-21100000000000000000000
χ534-4040000-444-4-400000044000000-4-400000000004i−4i00000004i−4i0000000000000000000000000000
χ544-4040000-444-4-400000044000000-4-40000000000−4i4i0000000−4i4i0000000000000000000000000000
χ554-40-200−2i32i3244-4-4000000-2-200−2i32i3−2i32i32200000000004i−4i0000023−23−2i2i0000000000000000000000000000
χ564-40-200−2i32i3244-4-4000000-2-200−2i32i3−2i32i3220000000000−4i4i00000−23232i−2i0000000000000000000000000000
χ574-40-2002i3−2i3244-4-4000000-2-2002i3−2i32i3−2i32200000000004i−4i00000−2323−2i2i0000000000000000000000000000
χ584-40-2002i3−2i3244-4-4000000-2-2002i3−2i32i3−2i3220000000000−4i4i0000023−232i−2i0000000000000000000000000000
χ59888-488-4-4-42-42-4-4-422-4-4-122-4-1-122-122-4-1-122-1-122000000000000000000000000000000000000000
χ60888-488-4-4-4-42-42-4-4-4-4222-1-4222-1-12-1-4222-1-122-1-1000000000000000000000000000000000000000
χ61888-4-8-8-4-4-42-42-444-2-244-122-4-1-122-12-2411-2-211-2-2000000000000000000000000000000000000000
χ62888-4-8-8-4-4-4-42-424444-2-22-1-4222-1-12-14-2-2-211-2-211000000000000000000000000000000000000000
χ6388-8-48-844-42-42-44-4-2-244-12-2411-2-2-122-411-2-2-1-122000000000000000000000000000000000000000
χ6488-8-48-844-4-42-424-444-2-22-14-2-2-2112-1-42-2-21122-1-1000000000000000000000000000000000000000
χ6588-8-4-8844-42-42-4-4422-4-4-12-2411-2-2-12-24-1-12211-2-2000000000000000000000000000000000000000
χ6688-8-4-8844-4-42-42-44-4-4222-14-2-2-2112-14-222-1-1-2-211000000000000000000000000000000000000000
χ678-8080000-82-4-24006i−6i002-4000000-24006i−6i000000000000000000000000000000000000000000000
χ688-8080000-82-4-2400−6i6i002-4000000-2400−6i6i000000000000000000000000000000000000000000000
χ698-8080000-8-424-200006i−6i-420000004-200006i−6i0000000000000000000000000000000000000000000
χ708-8080000-8-424-20000−6i6i-420000004-20000−6i6i0000000000000000000000000000000000000000000
χ718-80-400−4i34i342-4-24006i−6i00-1200−i3i32i3−2i31-200−3i3i0033−3300000000000000000000000000000000000000000
χ728-80-400−4i34i342-4-2400−6i6i00-1200−i3i32i3−2i31-2003i−3i00−333300000000000000000000000000000000000000000
χ738-80-400−4i34i34-424-200006i−6i2-1002i3−2i3−i3i3-210000−3i3i0033−33000000000000000000000000000000000000000
χ748-80-400−4i34i34-424-20000−6i6i2-1002i3−2i3−i3i3-2100003i−3i00−3333000000000000000000000000000000000000000
χ758-80-4004i3−4i342-4-24006i−6i00-1200i3−i3−2i32i31-200−3i3i00−333300000000000000000000000000000000000000000
χ768-80-4004i3−4i342-4-2400−6i6i00-1200i3−i3−2i32i31-2003i−3i0033−3300000000000000000000000000000000000000000
χ778-80-4004i3−4i34-424-200006i−6i2-100−2i32i3i3−i3-210000−3i3i00−3333000000000000000000000000000000000000000
χ788-80-4004i3−4i34-424-20000−6i6i2-100−2i32i3i3−i3-2100003i−3i0033−33000000000000000000000000000000000000000

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