Finite Group Databasebeta

← Group #10591396

Character table — Group #10591396

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222222222224444444444444444444444441212121212121212121212121212121212121212121212121818181818181818
order12222222334444666666666666663666666612121212121212121212121212121212444444441212121212121212121212121212121244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ81111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ9111-1-1-1-1111ii−i−i1111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−i1-11-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1
χ10111-1-1-1-1111ii−i−i1111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−i−ii1-1-11ii−i−i11-1-1−i−iii-1-111−i−iii-1-111
χ11111-1-1-1-1111ii−i−i1111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−iii−i-111-1−i−iii-1-111ii−i−i11-1-1−i−iii-1-111
χ12111-1-1-1-1111ii−i−i1111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii-11-11−i−iii-1-111−i−iii-1-111ii−i−i11-1-1
χ13111-1-1-1-1111−i−iii1111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−i-11-11ii−i−i-1-111ii−i−i-1-111−i−iii11-1-1
χ14111-1-1-1-1111−i−iii1111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−i−ii-111-1ii−i−i-1-111−i−iii11-1-1ii−i−i-1-111
χ15111-1-1-1-1111−i−iii1111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−iii−i1-1-11−i−iii11-1-1ii−i−i-1-111ii−i−i-1-111
χ16111-1-1-1-1111−i−iii1111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii1-11-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1
χ17222222222-1222222-1-122-1-12-12-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10022002200000000-1-1-1-1-1-1-1-100000000
χ18222222222-1222222-1-122-1-12-12-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-100-2-200-2-2000000001111111100000000
χ19222222222-1-2-2-2-222-1-122-1-12-12-12-1-1-1-1-1-1-1-1-1-2-211-2-21111111111002200-2-200000000-1-1-1-1111100000000
χ20222222222-1-2-2-2-222-1-122-1-12-12-12-1-1-1-1-1-1-1-1-1-2-211-2-2111111111100-2-20022000000001111-1-1-1-100000000
χ2122222222-122222-1-122-1-122-12-12-12-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122002200-1-1-1-1-1-1-1-10000000000000000
χ2222222222-122222-1-122-1-122-12-12-12-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-200-2-200111111110000000000000000
χ2322222222-12-2-2-2-2-1-122-1-122-12-12-12-1-1-1-1-1-1-1-111-2-211-2-2111111112200-2-200-1-1-1-111110000000000000000
χ2422222222-12-2-2-2-2-1-122-1-122-12-12-12-1-1-1-1-1-1-1-111-2-211-2-211111111-2-20022001111-1-1-1-10000000000000000
χ25222-2-2-2-222-12i2i−2i−2i22-1-1-2-211-212-1-21-1-1-1-111112i2i−i−i−2i−2iii−i−i−i−iiiii002i−2i002-200000000−i−iii-1-11100000000
χ26222-2-2-2-222-12i2i−2i−2i22-1-1-2-211-212-1-21-1-1-1-111112i2i−i−i−2i−2iii−i−i−i−iiiii00−2i2i00-2200000000ii−i−i11-1-100000000
χ27222-2-2-2-222-1−2i−2i2i2i22-1-1-2-211-212-1-21-1-1-1-11111−2i−2iii2i2i−i−iiiii−i−i−i−i002i−2i00-2200000000−i−iii11-1-100000000
χ28222-2-2-2-222-1−2i−2i2i2i22-1-1-2-211-212-1-21-1-1-1-11111−2i−2iii2i2i−i−iiiii−i−i−i−i00−2i2i002-200000000ii−i−i-1-11100000000
χ29222-2-2-2-22-122i2i−2i−2i-1-12211-2-21-2-121-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii2i−2i002-200−i−iii-1-1110000000000000000
χ30222-2-2-2-22-122i2i−2i−2i-1-12211-2-21-2-121-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii−2i2i00-2200ii−i−i11-1-10000000000000000
χ31222-2-2-2-22-12−2i−2i2i2i-1-12211-2-21-2-121-2-1-1-1-11111ii−2i−2i−i−i2i2iiiii−i−i−i−i2i−2i00-2200−i−iii11-1-10000000000000000
χ32222-2-2-2-22-12−2i−2i2i2i-1-12211-2-21-2-121-2-1-1-1-11111ii−2i−2i−i−i2i2iiiii−i−i−i−i−2i2i002-200ii−i−i-1-1110000000000000000
χ3322-222-2-2-2222-22-22-22-22-22-222-2-2-2-222-2-22-2-222-22-22-22-222-2-222-2-200000000000000000000000000000000
χ3422-222-2-2-222-22-222-22-22-22-222-2-2-2-222-2-22-2-22-22-22-22-22-2-222-2-22200000000000000000000000000000000
χ3522-222-2-2-22-12-22-22-2-112-2-112-1-21-21-1-111-111-12-2-112-2-11-1-111-1-11100000000000000003−33−33−33−300000000
χ3622-222-2-2-22-12-22-22-2-112-2-112-1-21-21-1-111-111-12-2-112-2-11-1-111-1-1110000000000000000−33−33−33−3300000000
χ3722-222-2-2-22-1-22-222-2-112-2-112-1-21-21-1-111-111-1-221-1-221-111-1-111-1-100000000000000003−33−3−33−3300000000
χ3822-222-2-2-22-1-22-222-2-112-2-112-1-21-21-1-111-111-1-221-1-221-111-1-111-1-10000000000000000−33−333−33−300000000
χ3922-222-2-2-2-122-22-2-112-2-112-2-121-21-2-1-111-111-1-112-2-112-2-1-111-1-111000000003−33−33−33−30000000000000000
χ4022-222-2-2-2-122-22-2-112-2-112-2-121-21-2-1-111-111-1-112-2-112-2-1-111-1-11100000000−33−33−33−330000000000000000
χ4122-222-2-2-2-12-22-22-112-2-112-2-121-21-2-1-111-111-11-1-221-1-2211-1-111-1-1000000003−33−3−33−330000000000000000
χ4222-222-2-2-2-12-22-22-112-2-112-2-121-21-2-1-111-111-11-1-221-1-2211-1-111-1-100000000−33−333−33−30000000000000000
χ4322-2-2-222-2222i−2i−2i2i2-22-2-22-22-2-2-2-22222-2-2-222-22i−2i2i−2i−2i2i−2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ4422-2-2-222-222−2i2i2i−2i2-22-2-22-22-2-2-2-22222-2-2-222-2−2i2i−2i2i2i−2i2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ4522-2-2-222-22-12i−2i−2i2i2-2-11-221-1-21-212-1-1-1111-1-112i−2i−ii−2i2ii−i−i−iiiii−i−i0000000000000000−i3i3i3−i3−333−300000000
χ4622-2-2-222-22-12i−2i−2i2i2-2-11-221-1-21-212-1-1-1111-1-112i−2i−ii−2i2ii−i−i−iiiii−i−i0000000000000000i3−i3−i3i33−3−3300000000
χ4722-2-2-222-22-1−2i2i2i−2i2-2-11-221-1-21-212-1-1-1111-1-11−2i2ii−i2i−2i−iiii−i−i−i−iii0000000000000000−i3i3i3−i33−3−3300000000
χ4822-2-2-222-22-1−2i2i2i−2i2-2-11-221-1-21-212-1-1-1111-1-11−2i2ii−i2i−2i−iiii−i−i−i−iii0000000000000000i3−i3−i3i3−333−300000000
χ4922-2-2-222-2-122i−2i−2i2i-112-21-1-221-21-2-12-1-1111-1-11−ii2i−2ii−i−2i2i−i−iiiii−i−i00000000−i3i3i3−i3−333−30000000000000000
χ5022-2-2-222-2-122i−2i−2i2i-112-21-1-221-21-2-12-1-1111-1-11−ii2i−2ii−i−2i2i−i−iiiii−i−i00000000i3−i3−i3i33−3−330000000000000000
χ5122-2-2-222-2-12−2i2i2i−2i-112-21-1-221-21-2-12-1-1111-1-11i−i−2i2i−ii2i−2iii−i−i−i−iii00000000−i3i3i3−i33−3−330000000000000000
χ5222-2-2-222-2-12−2i2i2i−2i-112-21-1-221-21-2-12-1-1111-1-11i−i−2i2i−ii2i−2iii−i−i−i−iii00000000i3−i3−i3i3−333−30000000000000000
χ532-222-2-22-2220000-22-222222-2-2-2-2-2-22-22-222-2-200000000000000000000000000000000000000002-22-20000
χ542-222-2-22-2220000-22-222222-2-2-2-2-2-22-22-222-2-20000000000000000000000000000000000000000-22-220000
χ552-22-222-2-2220000-22-22-2-2-2-222-2-2222-22-2-2-22200000000000000000000000000000000000000002i−2i−2i2i0000
χ562-22-222-2-2220000-22-22-2-2-2-222-2-2222-22-2-2-2220000000000000000000000000000000000000000−2i2i2i−2i0000
χ572-2-22-22-22220000-2-2-2-22-22-2-2-222222-2-222-22-2000000000000000000000000000000000000000000002-22-2
χ582-2-22-22-22220000-2-2-2-22-22-2-2-222222-2-222-22-200000000000000000000000000000000000000000000-22-22
χ592-2-2-22-222220000-2-2-2-2-22-222222-2-22-2-22-22-22000000000000000000000000000000000000000000002-2-22
χ602-2-2-22-222220000-2-2-2-2-22-222222-2-22-2-22-22-2200000000000000000000000000000000000000000000-222-2
χ6144444444-2-24444-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111-2-2-2-2-2-2-2-21111111100000000000000000000000000000000
χ6244444444-2-2-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111122222222-1-1-1-1-1-1-1-100000000000000000000000000000000
χ63444-4-4-4-44-2-24i4i−4i−4i-2-2-2-2222222-2-2221111-1-1-1-1−2i−2i−2i−2i2i2i2i2iiiii−i−i−i−i00000000000000000000000000000000
χ64444-4-4-4-44-2-2−4i−4i4i4i-2-2-2-2222222-2-2221111-1-1-1-12i2i2i2i−2i−2i−2i−2i−i−i−i−iiiii00000000000000000000000000000000
χ6544-444-4-4-4-2-24-44-4-22-22-22-22-2-2222211-1-11-1-11-22-22-22-2211-1-111-1-100000000000000000000000000000000
χ6644-444-4-4-4-2-2-44-44-22-22-22-22-2-2222211-1-11-1-112-22-22-22-2-1-111-1-11100000000000000000000000000000000
χ6744-4-4-444-4-2-24i−4i−4i4i-22-222-22-22222-2-211-1-1-111-1−2i2i−2i2i2i−2i2i−2iii−i−i−i−iii00000000000000000000000000000000
χ6844-4-4-444-4-2-2−4i4i4i−4i-22-222-22-22222-2-211-1-1-111-12i−2i2i−2i−2i2i−2i2i−i−iiiii−i−i00000000000000000000000000000000
χ694-444-4-44-44-20000-442-244-2-2-42-42-42-22-22-2-222000000000000000000000000000000000000000000000000
χ704-444-4-44-4-2400002-2-44-2-2442-42-42-4-22-22-2-222000000000000000000000000000000000000000000000000
χ714-444-4-44-4-2-200002-22-2-2-2-2-22222221-11-111-1-1000000003i−3i3i−3i3i−3i3i−3i00000000000000000000000000000000
χ724-444-4-44-4-2-200002-22-2-2-2-2-22222221-11-111-1-100000000−3i3i−3i3i−3i3i−3i3i00000000000000000000000000000000
χ734-44-444-4-44-20000-442-2-4-4224-2-424-2-22-2222-2-2000000000000000000000000000000000000000000000000
χ744-44-444-4-4-2400002-2-4422-4-4-242-4-24-22-2222-2-2000000000000000000000000000000000000000000000000
χ754-44-444-4-4-2-200002-22-22222-2-222-2-21-11-1-1-111000000003-33-3-33-3300000000000000000000000000000000
χ764-44-444-4-4-2-200002-22-22222-2-222-2-21-11-1-1-11100000000-33-333-33-300000000000000000000000000000000
χ774-4-44-44-444-20000-4-4224-4-22-424-24-2-222-2-22-22000000000000000000000000000000000000000000000000
χ784-4-44-44-44-24000022-4-4-224-42-4-24-24-222-2-22-22000000000000000000000000000000000000000000000000
χ794-4-44-44-44-2-200002222-22-2222-2-2-2-21-1-111-11-1000000003i−3i−3i3i3i−3i−3i3i00000000000000000000000000000000
χ804-4-44-44-44-2-200002222-22-2222-2-2-2-21-1-111-11-100000000−3i3i3i−3i−3i3i3i−3i00000000000000000000000000000000
χ814-4-4-44-4444-20000-4-422-442-24-24-2-42-222-22-22-2000000000000000000000000000000000000000000000000
χ824-4-4-44-444-24000022-4-42-2-44-24-242-4-222-22-22-2000000000000000000000000000000000000000000000000
χ834-4-4-44-444-2-2000022222-22-2-2-2-2-2221-1-11-11-11000000003-3-33-333-300000000000000000000000000000000
χ844-4-4-44-444-2-2000022222-22-2-2-2-2-2221-1-11-11-1100000000-333-33-3-3300000000000000000000000000000000

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