Finite Group Databasebeta

← Group #10591360

Character table — Group #10591360

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222222222224444444444444444444444441212121212121212121212121212121212121212121212121818181818181818
order12222222334444666666666666663666666612121212121212121212121212121212444444441212121212121212121212121212121244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ51111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91-1-11-1-1111111-1-11111-1-1-1-111-1-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ101-1-11-1-1111111-1-11111-1-1-1-111-1-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-1i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ111-1-11-1-1111111-1-11111-1-1-1-111-1-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-1−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ121-1-11-1-1111111-1-11111-1-1-1-111-1-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ131-1-11-1-11111-1-1111111-1-1-1-111-1-1-1-1111-1-1-1-11-1-1-1-11111-1-1-1-11111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ141-1-11-1-11111-1-1111111-1-1-1-111-1-1-1-1111-1-1-1-11-1-1-1-11111-1-1-1-11111i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ151-1-11-1-11111-1-1111111-1-1-1-111-1-1-1-1111-1-1-1-11-1-1-1-11111-1-1-1-11111−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ161-1-11-1-11111-1-1111111-1-1-1-111-1-1-1-1111-1-1-1-11-1-1-1-11111-1-1-1-11111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
χ17222222222-1222222-1-122-1-12-122-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-100000000
χ18222222222-1222222-1-122-1-12-122-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000001111111100000000
χ19222222222-1-2-2-2-222-1-122-1-12-122-1-1-1-1-1-1-1-1-1-1-2-211-2-21111111111000022-2-200000000-1-1-1-1111100000000
χ20222222222-1-2-2-2-222-1-122-1-12-122-1-1-1-1-1-1-1-1-1-1-2-211-2-211111111110000-2-222000000001111-1-1-1-100000000
χ2122222222-122222-1-122-1-122-12-1-122-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-10000000000000000
χ2222222222-122222-1-122-1-122-12-1-122-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-2-2-20000111111110000000000000000
χ2322222222-12-2-2-2-2-1-122-1-122-12-1-122-1-1-1-1-1-1-1-111-2-211-2-21111111122-2-20000-1-1-1-111110000000000000000
χ2422222222-12-2-2-2-2-1-122-1-122-12-1-122-1-1-1-1-1-1-1-111-2-211-2-211111111-2-22200001111-1-1-1-10000000000000000
χ25222-2-2-22-22200002-22-22222-2-2-2-2-2-222-222-2-2-2000000000000000000000000000000000000000000002-22-2
χ26222-2-2-22-22200002-22-22222-2-2-2-2-2-222-222-2-2-200000000000000000000000000000000000000000000-22-22
χ2722-222-2-2-2220000-2-2-2-22-22-2222-22-22-2-22-22-2200000000000000000000000000000000000000002i−2i2i−2i0000
χ2822-222-2-2-2220000-2-2-2-22-22-2222-22-22-2-22-22-220000000000000000000000000000000000000000−2i2i−2i2i0000
χ2922-2-2-22-22222i−2i2i−2i-22-222-22-2-2-2-22-222-222-2-22-22i−2i2i−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ3022-2-2-22-2222−2i2i−2i2i-22-222-22-2-2-2-22-222-222-2-22-2−2i2i−2i2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ3122-2-2-22-222-12i−2i2i−2i-221-12-2-11-21-221-1-11-1-111-112i−2i−ii2i−2i−ii−i−iii−i−iii0000000000000000−i3i3−i3i33−33−300000000
χ3222-2-2-22-222-12i−2i2i−2i-221-12-2-11-21-221-1-11-1-111-112i−2i−ii2i−2i−ii−i−iii−i−iii0000000000000000i3−i3i3−i3−33−3300000000
χ3322-2-2-22-222-1−2i2i−2i2i-221-12-2-11-21-221-1-11-1-111-11−2i2ii−i−2i2ii−iii−i−iii−i−i0000000000000000−i3i3−i3i3−33−3300000000
χ3422-2-2-22-222-1−2i2i−2i2i-221-12-2-11-21-221-1-11-1-111-11−2i2ii−i−2i2ii−iii−i−iii−i−i0000000000000000i3−i3i3−i33−33−300000000
χ3522-2-2-22-22-122i−2i2i−2i1-1-22-112-21-21-1-22-11-1-111-11−ii2i−2i−ii2i−2i−i−iii−i−iii000000003−33−3−i3i3−i3i30000000000000000
χ3622-2-2-22-22-122i−2i2i−2i1-1-22-112-21-21-1-22-11-1-111-11−ii2i−2i−ii2i−2i−i−iii−i−iii00000000−33−33i3−i3i3−i30000000000000000
χ3722-2-2-22-22-12−2i2i−2i2i1-1-22-112-21-21-1-22-11-1-111-11i−i−2i2ii−i−2i2iii−i−iii−i−i000000003−33−3i3−i3i3−i30000000000000000
χ3822-2-2-22-22-12−2i2i−2i2i1-1-22-112-21-21-1-22-11-1-111-11i−i−2i2ii−i−2i2iii−i−iii−i−i00000000−33−33−i3i3−i3i30000000000000000
χ392-222-22-2-2220000-2-2-2-2-22-2222-22-222-2-2-22-22200000000000000000000000000000000000000002i−2i−2i2i0000
χ402-222-22-2-2220000-2-2-2-2-22-2222-22-222-2-2-22-2220000000000000000000000000000000000000000−2i2i2i−2i0000
χ412-22-22-2-22222i−2i−2i2i-22-22-22-22-2-22-22-22-22-222-2-22i−2i2i−2i−2i2i−2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ422-22-22-2-2222−2i2i2i−2i-22-22-22-22-2-22-22-22-22-222-2-2−2i2i−2i2i2i−2i2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ432-22-22-2-222-12i−2i−2i2i-221-1-221-1-212-2-11-11-11-1-1112i−2i−ii−2i2ii−i−i−iiiii−i−i00000000000000003−3−33i3−i3−i3i300000000
χ442-22-22-2-222-12i−2i−2i2i-221-1-221-1-212-2-11-11-11-1-1112i−2i−ii−2i2ii−i−i−iiiii−i−i0000000000000000−333−3−i3i3i3−i300000000
χ452-22-22-2-222-1−2i2i2i−2i-221-1-221-1-212-2-11-11-11-1-111−2i2ii−i2i−2i−iiii−i−i−i−iii00000000000000003−3−33−i3i3i3−i300000000
χ462-22-22-2-222-1−2i2i2i−2i-221-1-221-1-212-2-11-11-11-1-111−2i2ii−i2i−2i−iiii−i−i−i−iii0000000000000000−333−3i3−i3−i3i300000000
χ472-22-22-2-22-122i−2i−2i2i1-1-221-1-221-2-112-2-11-11-1-111−ii2i−2ii−i−2i2i−i−iiiii−i−i00000000−i3i3i3−i3−333−30000000000000000
χ482-22-22-2-22-122i−2i−2i2i1-1-221-1-221-2-112-2-11-11-1-111−ii2i−2ii−i−2i2i−i−iiiii−i−i00000000i3−i3−i3i33−3−330000000000000000
χ492-22-22-2-22-12−2i2i2i−2i1-1-221-1-221-2-112-2-11-11-1-111i−i−2i2i−ii2i−2iii−i−i−i−iii00000000−i3i3i3−i33−3−330000000000000000
χ502-22-22-2-22-12−2i2i2i−2i1-1-221-1-221-2-112-2-11-11-1-111i−i−2i2i−ii2i−2iii−i−i−i−iii00000000i3−i3−i3i3−333−30000000000000000
χ512-2-22-2-2222-122-2-222-1-1-2-2112-1-2-211-1-1-11111-122-1-1-2-211-1-1-1-1111100002i−2i2i−2i00000000−i−iii−i−iii00000000
χ522-2-22-2-2222-122-2-222-1-1-2-2112-1-2-211-1-1-11111-122-1-1-2-211-1-1-1-111110000−2i2i−2i2i00000000ii−i−iii−i−i00000000
χ532-2-22-2-2222-1-2-22222-1-1-2-2112-1-2-211-1-1-11111-1-2-21122-1-11111-1-1-1-100002i−2i−2i2i00000000−i−iiiii−i−i00000000
χ542-2-22-2-2222-1-2-22222-1-1-2-2112-1-2-211-1-1-11111-1-2-21122-1-11111-1-1-1-10000−2i2i2i−2i00000000ii−i−i−i−iii00000000
χ552-2-22-2-222-1222-2-2-1-12211-2-2-1211-2-2-1-1-11111-1-1-12211-2-2-1-1-1-111112i−2i2i−2i0000−i−iii−i−iii0000000000000000
χ562-2-22-2-222-1222-2-2-1-12211-2-2-1211-2-2-1-1-11111-1-1-12211-2-2-1-1-1-11111−2i2i−2i2i0000ii−i−iii−i−i0000000000000000
χ572-2-22-2-222-12-2-222-1-12211-2-2-1211-2-2-1-1-11111-111-2-2-1-1221111-1-1-1-12i−2i−2i2i0000−i−iiiii−i−i0000000000000000
χ582-2-22-2-222-12-2-222-1-12211-2-2-1211-2-2-1-1-11111-111-2-2-1-1221111-1-1-1-1−2i2i2i−2i0000ii−i−i−i−iii0000000000000000
χ592-2-2-2222-22200002-22-2-2-2-2-2-2-2222222-2-2-222-2000000000000000000000000000000000000000000002-2-22
χ602-2-2-2222-22200002-22-2-2-2-2-2-2-2222222-2-2-222-200000000000000000000000000000000000000000000-222-2
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
χ63444-4-4-44-44-200004-4-2244-2-2-42-4-422-2-22-2-2222000000000000000000000000000000000000000000000000
χ64444-4-4-44-4-240000-224-4-2-2442-422-4-4-2-22-2-2222000000000000000000000000000000000000000000000000
χ65444-4-4-44-4-2-20000-22-22-2-2-2-222222211-111-1-1-1000000003i−3i3i−3i3i−3i3i−3i00000000000000000000000000000000
χ66444-4-4-44-4-2-20000-22-22-2-2-2-222222211-111-1-1-100000000−3i3i−3i3i−3i3i−3i3i00000000000000000000000000000000
χ6744-444-4-4-44-20000-4-4224-4-224-24-4-22-222-22-22-2000000000000000000000000000000000000000000000000
χ6844-444-4-4-4-24000022-4-4-224-4-24-224-4-222-22-22-2000000000000000000000000000000000000000000000000
χ6944-444-4-4-4-2-200002222-22-22-2-2-22-221-1-11-11-11000000003-3-333-3-3300000000000000000000000000000000
χ7044-444-4-4-4-2-200002222-22-22-2-2-22-221-1-11-11-1100000000-333-3-333-300000000000000000000000000000000
χ7144-4-4-44-44-2-24i−4i4i−4i2-22-2-22-22222-22-21-111-1-11-1−2i2i−2i2i−2i2i−2i2iii−i−iii−i−i00000000000000000000000000000000
χ7244-4-4-44-44-2-2−4i4i−4i4i2-22-2-22-22222-22-21-111-1-11-12i−2i2i−2i2i−2i2i−2i−i−iii−i−iii00000000000000000000000000000000
χ734-444-44-4-44-20000-4-422-442-24-2-442-2-2222-22-2-2000000000000000000000000000000000000000000000000
χ744-444-44-4-4-24000022-4-42-2-44-242-2-44-2222-22-2-2000000000000000000000000000000000000000000000000
χ754-444-44-4-4-2-2000022222-22-2-2-22-22-21-1-1-11-111000000003-3-33-333-300000000000000000000000000000000
χ764-444-44-4-4-2-2000022222-22-2-2-22-22-21-1-1-11-11100000000-333-33-3-3300000000000000000000000000000000
χ774-44-44-4-44-2-24i−4i−4i4i2-22-22-22-222-22-221-11-111-1-1−2i2i−2i2i2i−2i2i−2iii−i−i−i−iii00000000000000000000000000000000
χ784-44-44-4-44-2-2−4i4i4i−4i2-22-22-22-222-22-221-11-111-1-12i−2i2i−2i−2i2i−2i2i−i−iiiii−i−i00000000000000000000000000000000
χ794-4-44-4-444-2-244-4-4-2-2-2-22222-2-22222111-1-1-1-11-2-2-2-222221111-1-1-1-100000000000000000000000000000000
χ804-4-44-4-444-2-2-4-444-2-2-2-22222-2-22222111-1-1-1-112222-2-2-2-2-1-1-1-1111100000000000000000000000000000000
χ814-4-4-4444-44-200004-4-22-4-422-4244-2-2-2-2222-2-22000000000000000000000000000000000000000000000000
χ824-4-4-4444-4-240000-224-422-4-42-4-2-244-2-2222-2-22000000000000000000000000000000000000000000000000
χ834-4-4-4444-4-2-20000-22-22222222-2-2-2-211-1-1-111-1000000003i−3i3i−3i−3i3i−3i3i00000000000000000000000000000000
χ844-4-4-4444-4-2-20000-22-22222222-2-2-2-211-1-1-111-100000000−3i3i−3i3i3i−3i3i−3i00000000000000000000000000000000

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