Finite Group Databasebeta

← Group #72271673

Character table — Group #72271673

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111111122226666666666661212121212121212121212121212242424242424242432323232323232323232323232323232484848484848484848484848
order12222222222222224444444422222222224444444444443666666666666666444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ5111-1-11-1-111-1-111-1-11111-1-1-1-111-1-1111-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−i
χ6111-1-11-1-111-1-111-1-11111-1-1-1-111-1-1111-1-1-111-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii
χ7111-1-11-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1111-1-111ii−i−i−i−iii1111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iii
χ8111-1-11-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1111-1-111−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i
χ92222222222222222222222222222222222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1022222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-111111111000000000000
χ11222-2-22-2-222-2-222-2-22222-2-2-2-222-2-2222-2-2-222-2-200000000-1-1-1-11111-1-1-1-11111000000000000
χ12222-2-22-2-2-2-22222-2-22222-2-2-2-222-2-2-2-2-2222-2-22200000000-1-1-1-111111111-1-1-1-1000000000000
χ132-2-22-222-200002-22-222-2-222-2-22-22-200000000000000000022-2-222-2-200000000000000000000
χ142-2-22-222-200002-22-222-2-222-2-22-22-2000000000000000000-1-111-1-111−i3−i3i3i3−i3−i3i3i3000000000000
χ152-2-22-222-200002-22-222-2-222-2-22-22-2000000000000000000-1-111-1-111i3i3−i3−i3i3i3−i3−i3000000000000
χ162-2-2-222-2200002-2-2222-2-2-2-2222-2-2200000000000000000022-2-2-2-22200000000000000000000
χ172-2-2-222-2200002-2-2222-2-2-2-2222-2-22000000000000000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3000000000000
χ182-2-2-222-2200002-2-2222-2-2-2-2222-2-22000000000000000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3000000000000
χ193333333333333333-1-1-1-1-1-1-1-1-1-1-1-13-1-13-1-1-1-1-1-11111111100000000000000001111-1-1-1-1-1-1-1-1
χ203333333333333333-1-1-1-1-1-1-1-1-1-1-1-13-1-13-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-111111111
χ21333333333333-1-1-1-13-13-13-13-1-1-1-1-1-1-1-1-1-1-13-13-1111111110000000000000000-1-1-1-11-11-11-11-1
χ22333333333333-1-1-1-13-13-13-13-1-1-1-1-1-1-1-1-1-1-13-13-1-1-1-1-1-1-1-1-100000000000000001111-11-11-11-11
χ23333333333333-1-1-1-1-13-13-13-13-1-1-1-1-1-1-1-1-1-1-13-13111111110000000000000000-1-1-1-1-11-11-11-11
χ24333333333333-1-1-1-1-13-13-13-13-1-1-1-1-1-1-1-1-1-1-13-13-1-1-1-1-1-1-1-1000000000000000011111-11-11-11-1
χ2533333333-3-3-3-33333-1-1-1-1-1-1-1-1-1-1-1-1-311-31111111111-1-1-1-1000000000000000011-1-1-1-1-1-11111
χ2633333333-3-3-3-33333-1-1-1-1-1-1-1-1-1-1-1-1-311-3111111-1-1-1-111110000000000000000-1-1111111-1-1-1-1
χ2733333333-3-3-3-3-1-1-1-13-13-13-13-1-1-1-1-1111111-31-311111-1-1-1-10000000000000000-1-1111-11-1-11-11
χ2833333333-3-3-3-3-1-1-1-13-13-13-13-1-1-1-1-1111111-31-31-1-1-1-11111000000000000000011-1-1-11-111-11-1
χ2933333333-3-3-3-3-1-1-1-1-13-13-13-13-1-1-1-11111111-31-31111-1-1-1-10000000000000000-1-111-11-111-11-1
χ3033333333-3-3-3-3-1-1-1-1-13-13-13-13-1-1-1-11111111-31-3-1-1-1-11111000000000000000011-1-11-11-1-11-11
χ31333-3-33-3-333-3-333-3-3-1-1-1-11111-1-1113-1-1-311-1-111ii−i−iii−i−i0000000000000000i−ii−i−i−iii−i−iii
χ32333-3-33-3-333-3-333-3-3-1-1-1-11111-1-1113-1-1-311-1-111−i−iii−i−iii0000000000000000−ii−iiii−i−iii−i−i
χ33333-3-33-3-333-3-3-1-1113-13-1-31-31-1-111-1-1-11113-1-31ii−i−iii−i−i0000000000000000−ii−iii−i−iii−i−ii
χ34333-3-33-3-333-3-3-1-1113-13-1-31-31-1-111-1-1-11113-1-31−i−iii−i−iii0000000000000000i−ii−i−iii−i−iii−i
χ35333-3-33-3-333-3-3-1-111-13-131-31-3-1-111-1-1-1111-131-3ii−i−iii−i−i0000000000000000−ii−ii−iii−i−iii−i
χ36333-3-33-3-333-3-3-1-111-13-131-31-3-1-111-1-1-1111-131-3−i−iii−i−iii0000000000000000i−ii−ii−i−iii−i−ii
χ37333-3-33-3-3-3-33333-3-3-1-1-1-11111-1-111-3113-1-111-1-1ii−i−i−i−iii0000000000000000i−i−ii−i−iiiii−i−i
χ38333-3-33-3-3-3-33333-3-3-1-1-1-11111-1-111-3113-1-111-1-1−i−iiiii−i−i0000000000000000−iii−iii−i−i−i−iii
χ39333-3-33-3-3-3-333-1-1113-13-1-31-31-1-111111-1-1-1-313-1ii−i−i−i−iii0000000000000000−iii−ii−i−ii−iii−i
χ40333-3-33-3-3-3-333-1-1113-13-1-31-31-1-111111-1-1-1-313-1−i−iiiii−i−i0000000000000000i−i−ii−iii−ii−i−ii
χ41333-3-33-3-3-3-333-1-111-13-131-31-3-1-111111-1-1-11-3-13ii−i−i−i−iii0000000000000000−iii−i−iii−ii−i−ii
χ42333-3-33-3-3-3-333-1-111-13-131-31-3-1-111111-1-1-11-3-13−i−iiiii−i−i0000000000000000i−i−iii−i−ii−iii−i
χ4344-444-4-4-44-44-4000000000000000000000000002i−2i2i−2i2i−2i2i−2i1-11-11-11-11-11-11-11-1000000000000
χ4444-444-4-4-44-44-400000000000000000000000000−2i2i−2i2i−2i2i−2i2i1-11-11-11-11-11-11-11-1000000000000
χ4544-444-4-4-4-44-44000000000000000000000000002i−2i2i−2i−2i2i−2i2i1-11-11-11-1-11-11-11-11000000000000
χ4644-444-4-4-4-44-4400000000000000000000000000−2i2i−2i2i2i−2i2i−2i1-11-11-11-1-11-11-11-11000000000000
χ4744-4-4-4-4444-4-44000000000000000000000000002-2-222-2-221-11-1-11-111-11-1-11-11000000000000
χ4844-4-4-4-4444-4-4400000000000000000000000000-222-2-222-21-11-1-11-111-11-1-11-11000000000000
χ4944-4-4-4-444-444-4000000000000000000000000002-2-22-222-21-11-1-11-11-11-111-11-1000000000000
χ5044-4-4-4-444-444-400000000000000000000000000-222-22-2-221-11-1-11-11-11-111-11-1000000000000
χ51666666666666-2-2-2-2-2-2-2-2-2-2-2-22222-222-222-2-2-2-2000000000000000000000000000000000000
χ5266666666-6-6-6-6-2-2-2-2-2-2-2-2-2-2-2-222222-2-22-2-22222000000000000000000000000000000000000
χ53666-6-66-6-666-6-6-2-222-2-2-2-2222222-2-2-2222-2-2-2-222000000000000000000000000000000000000
χ54666-6-66-6-6-6-666-2-222-2-2-2-2222222-2-22-2-2-22222-2-2000000000000000000000000000000000000
χ556-6-66-666-600006-66-6-2-222-2-222-22-220000000000000000000000000000000000000000000000
χ566-6-66-666-60000-22-226-2-626-2-62-22-220000000000000000000000000000000000000000000000
χ576-6-66-666-60000-22-22-262-6-262-6-22-220000000000000000000000000000000000000000000000
χ586-6-66-666-60000-22-22-2-222-2-2222-22-204-404-40000000000000000000000000000000000000000
χ596-6-66-666-60000-22-22-2-222-2-2222-22-20-440-440000000000000000000000000000000000000000
χ606-6-6-666-6600006-6-66-2-22222-2-2-222-20000000000000000000000000000000000000000000000
χ616-6-6-666-660000-222-26-2-62-626-2-222-20000000000000000000000000000000000000000000000
χ626-6-6-666-660000-222-2-262-62-6-26-222-20000000000000000000000000000000000000000000000
χ636-6-6-666-660000-222-2-2-22222-2-22-2-2204-40-440000000000000000000000000000000000000000
χ646-6-6-666-660000-222-2-2-22222-2-22-2-220-4404-40000000000000000000000000000000000000000
χ6588-888-8-8-88-88-80000000000000000000000000000000000-11-11-11-11-11-11-11-11000000000000
χ6688-888-8-8-8-88-880000000000000000000000000000000000-11-11-11-111-11-11-11-1000000000000
χ6788-8-8-8-8888-8-880000000000000000000000000000000000-11-111-11-1-11-111-11-1000000000000
χ6888-8-8-8-888-888-80000000000000000000000000000000000-11-111-11-11-11-1-11-11000000000000
χ698-888-8-8-88000000000000000000000000000000000000002-2-222-2-2200000000000000000000
χ708-888-8-8-8800000000000000000000000000000000000000-111-1-111-1−i3i3i3−i3−i3i3i3−i3000000000000
χ718-888-8-8-8800000000000000000000000000000000000000-111-1-111-1i3−i3−i3i3i3−i3−i3i3000000000000
χ728-88-88-88-8000000000000000000000000000000000000002-2-22-222-200000000000000000000
χ738-88-88-88-800000000000000000000000000000000000000-111-11-1-11−i3i3i3−i3i3−i3−i3i3000000000000
χ748-88-88-88-800000000000000000000000000000000000000-111-11-1-11i3−i3−i3i3−i3i3i3−i3000000000000

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