Finite Group Databasebeta

← Group #10591009

Character table — Group #10591009

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11112222222222444444444488888888881212121212121212121212121212121218181818242424243636
order124423346612121212366688121212126122424242424242424224444441212121212121212224466121288
χ1111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-11-111-1-11111-1-1-1-1-1-1-1-11-11-1-1-1
χ31111111111111111111111111111111111-11-11-1-111-1-1-1-11111-1-1-1-1-11-11-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ6111111111111111111-1-1111111-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-11111-1-1-1-11-11-111
χ7111111111111111111-1-1111111-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-1-1-1-1-1-11-1111
χ8111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ911-1-1-111111-1-1-1-111-1-1i−i11-1-1-11ii−i−iii−i−i11-1-1i−ii−iii−i−iii−i−i1-11-111-1-1i−i
χ1011-1-1-111111-1-1-1-111-1-1i−i11-1-1-11ii−i−iii−i−i1-1-11i−i−iiii−i−i−i−iii-11-111-1-11−ii
χ1111-1-1-111111-1-1-1-111-1-1i−i11-1-1-11ii−i−iii−i−i-111-1−iii−i−i−iiiii−i−i-11-11-111-1−ii
χ1211-1-1-111111-1-1-1-111-1-1i−i11-1-1-11ii−i−iii−i−i-1-111−ii−ii−i−iii−i−iii1-11-1-1-111i−i
χ1311-1-1-111111-1-1-1-111-1-1−ii11-1-1-11−i−iii−i−iii11-1-1−ii−ii−i−iii−i−iii1-11-111-1-1−ii
χ1411-1-1-111111-1-1-1-111-1-1−ii11-1-1-11−i−iii−i−iii1-1-11−iii−i−i−iiiii−i−i-11-111-1-11i−i
χ1511-1-1-111111-1-1-1-111-1-1−ii11-1-1-11−i−iii−i−iii-111-1i−i−iiii−i−i−i−iii-11-11-111-1i−i
χ1611-1-1-111111-1-1-1-111-1-1−ii11-1-1-11−i−iii−i−iii-1-111i−ii−iii−i−iii−i−i1-11-1-1-111−ii
χ17222222-122-122-1-1-1-12-1222-1-1-1-1-12-12-1-1-1-1-1020200220000-1-1-1-100000-10-100
χ18222222-122-122-1-1-1-12-1222-1-1-1-1-12-12-1-1-1-1-10-20-200-2-2000011110000010100
χ19222222-122-122-1-1-1-12-1-2-22-1-1-1-1-1-21-211111020200-2-20000111100000-10-100
χ20222222-122-122-1-1-1-12-1-2-22-1-1-1-1-1-21-2111110-20-200220000-1-1-1-10000010100
χ2122222-122-12-1-122-1-1-1222-12-1-1-1-1-12-12-1-1-1-120202200-1-1-1-100000000-10-1000
χ2222222-122-12-1-122-1-1-1222-12-1-1-1-1-12-12-1-1-1-1-20-20-2-200111100000000101000
χ2322222-122-12-1-122-1-1-12-2-2-12-1-1-1-11-21-211112020-2-200111100000000-10-1000
χ2422222-122-12-1-122-1-1-12-2-2-12-1-1-1-11-21-21111-20-202200-1-1-1-100000000101000
χ252222-222-222222222-2-200-2-222-2-20000000000000000000000002-2-22000000
χ262222-222-222222222-2-200-2-222-2-2000000000000000000000000-222-2000000
χ2722-2-2222-222-2-2-2-2222200-2-2-2-22-200000000000000000000000022-2-2000000
χ2822-2-2222-222-2-2-2-2222200-2-2-2-22-2000000000000000000000000-2-222000000
χ2922-2-2-22-122-1-2-211-1-1-212i−2i2-1111-12i−i−2ii−i−iii020-2002i−2i0000−i−iii00000-10100
χ3022-2-2-22-122-1-2-211-1-1-212i−2i2-1111-12i−i−2ii−i−iii0-20200−2i2i0000ii−i−i0000010-100
χ3122-2-2-22-122-1-2-211-1-1-21−2i2i2-1111-1−2ii2i−iii−i−i020-200−2i2i0000ii−i−i00000-10100
χ3222-2-2-22-122-1-2-211-1-1-21−2i2i2-1111-1−2ii2i−iii−i−i0-202002i−2i0000−i−iii0000010-100
χ3322-2-2-2-122-1211-2-2-1-11-22i−2i-12111-1−i2ii−2i−i−iii20-202i−2i00−i−iii00000000-101000
χ3422-2-2-2-122-1211-2-2-1-11-22i−2i-12111-1−i2ii−2i−i−iii-2020−2i2i00ii−i−i0000000010-1000
χ3522-2-2-2-122-1211-2-2-1-11-2−2i2i-12111-1i−2i−i2iii−i−i20-20−2i2i00ii−i−i00000000-101000
χ3622-2-2-2-122-1211-2-2-1-11-2−2i2i-12111-1i−2i−i2iii−i−i-20202i−2i00−i−iii0000000010-1000
χ3744444-2-24-2-2-2-2-2-211-2-244-2-21111-2-2-2-2111100000000000000000000000000
χ3844444-2-24-2-2-2-2-2-211-2-2-4-4-2-211112222-1-1-1-100000000000000000000000000
χ394444-44-2-44-244-2-2-2-2-4200-42-2-2220000000000000000000000000000000000
χ404444-4-24-4-24-2-244-2-22-4002-4-2-2220000000000000000000000000000000000
χ414444-4-2-2-4-2-2-2-2-2-21122002211-1-100003-33-300000000000000000000000000
χ424444-4-2-2-4-2-2-2-2-2-21122002211-1-10000-33-3300000000000000000000000000
χ4344-4-444-2-44-2-4-422-2-24-200-4222-220000000000000000000000000000000000
χ4444-4-44-24-4-2422-4-4-2-2-24002-422-220000000000000000000000000000000000
χ4544-4-44-2-2-4-2-2222211-2-20022-1-11-100003i−3i−3i3i00000000000000000000000000
χ4644-4-44-2-2-4-2-2222211-2-20022-1-11-10000−3i3i3i−3i00000000000000000000000000
χ4744-4-4-4-2-24-2-2222211224i−4i-2-2-1-1-11−2i−2i2i2iii−i−i00000000000000000000000000
χ4844-4-4-4-2-24-2-222221122−4i4i-2-2-1-1-112i2i−2i−2i−i−iii00000000000000000000000000
χ494-44i−4i0440-4-44i−4i4i−4i4-40000004i−4i000000000000000000000000000000000000
χ504-44i−4i04-20-424i−4i−2i2i-22000000−2i2i0000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000
χ514-44i−4i04-20-424i−4i−2i2i-22000000−2i2i0000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000
χ524-44i−4i0-2402-4−2i2i4i−4i-22000000−2i2i000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000000000
χ534-44i−4i0-2402-4−2i2i4i−4i-22000000−2i2i000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000000000
χ544-4−4i4i0440-4-4−4i4i−4i4i4-4000000−4i4i000000000000000000000000000000000000
χ554-4−4i4i04-20-42−4i4i2i−2i-220000002i−2i0000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000
χ564-4−4i4i04-20-42−4i4i2i−2i-220000002i−2i0000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000
χ574-4−4i4i0-2402-42i−2i−4i4i-220000002i−2i000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000000000
χ584-4−4i4i0-2402-42i−2i−4i4i-220000002i−2i000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000000000
χ598-88i−8i0-4-4044−4i4i−4i4i2-20000002i−2i000000000000000000000000000000000000
χ608-8−8i8i0-4-40444i−4i4i−4i2-2000000−2i2i000000000000000000000000000000000000

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