Finite Group Databasebeta

← Group #10591219

Character table — Group #10591219

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222222222224444444444444444444444441212121212121212121212121212121212121212121212121818181818181818
order12222222334444666666666666663666666612121212121212121212121212121212444444441212121212121212121212121212121222224444
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
χ9111-1-1-1-111111-1-11111-1-1-1-111-1-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ10111-1-1-1-111111-1-11111-1-1-1-111-1-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-1i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ11111-1-1-1-111111-1-11111-1-1-1-111-1-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-1−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ12111-1-1-1-111111-1-11111-1-1-1-111-1-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ13111-1-1-1-1111-1-1111111-1-1-1-111-1-1-1-1111-1-1-1-11-1-1-1-11111-1-1-1-11111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ14111-1-1-1-1111-1-1111111-1-1-1-111-1-1-1-1111-1-1-1-11-1-1-1-11111-1-1-1-11111i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ15111-1-1-1-1111-1-1111111-1-1-1-111-1-1-1-1111-1-1-1-11-1-1-1-11111-1-1-1-11111−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ16111-1-1-1-1111-1-1111111-1-1-1-111-1-1-1-1111-1-1-1-11-1-1-1-11111-1-1-1-11111−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
χ25222-2-2-2-222-122-2-222-1-1-2-2112-1-2-211-1-1-11111-122-1-1-2-211-1-1-1-1111100002i−2i2i−2i00000000−i−iii−i−iii00000000
χ26222-2-2-2-222-122-2-222-1-1-2-2112-1-2-211-1-1-11111-122-1-1-2-211-1-1-1-111110000−2i2i−2i2i00000000ii−i−iii−i−i00000000
χ27222-2-2-2-222-1-2-22222-1-1-2-2112-1-2-211-1-1-11111-1-2-21122-1-11111-1-1-1-100002i−2i−2i2i00000000−i−iiiii−i−i00000000
χ28222-2-2-2-222-1-2-22222-1-1-2-2112-1-2-211-1-1-11111-1-2-21122-1-11111-1-1-1-10000−2i2i2i−2i00000000ii−i−i−i−iii00000000
χ29222-2-2-2-22-1222-2-2-1-12211-2-2-1211-2-2-1-1-11111-1-1-12211-2-2-1-1-1-111112i−2i2i−2i0000−i−iii−i−iii0000000000000000
χ30222-2-2-2-22-1222-2-2-1-12211-2-2-1211-2-2-1-1-11111-1-1-12211-2-2-1-1-1-11111−2i2i−2i2i0000ii−i−iii−i−i0000000000000000
χ31222-2-2-2-22-12-2-222-1-12211-2-2-1211-2-2-1-1-11111-111-2-2-1-1221111-1-1-1-12i−2i−2i2i0000−i−iiiii−i−i0000000000000000
χ32222-2-2-2-22-12-2-222-1-12211-2-2-1211-2-2-1-1-11111-111-2-2-1-1221111-1-1-1-1−2i2i2i−2i0000ii−i−i−i−iii0000000000000000
χ3322-222-2-2-22200002-22-222-2-2-2-2-2-22222-222-2-2-2000000000000000000000000000000000000000000002i−2i2i−2i
χ3422-222-2-2-22200002-22-222-2-2-2-2-2-22222-222-2-2-200000000000000000000000000000000000000000000−2i2i−2i2i
χ3522-2-2-222-22200002-22-2-2-222-2-222-2-222-2-2-222-2000000000000000000000000000000000000000000002i−2i−2i2i
χ3622-2-2-222-22200002-22-2-2-222-2-222-2-222-2-2-222-200000000000000000000000000000000000000000000−2i2i2i−2i
χ372-222-22-2-2222i−2i2i−2i-22-222-22-2-2-22-22-22-222-22-2-22i−2i2i−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ382-222-22-2-222−2i2i−2i2i-22-222-22-2-2-22-22-22-222-22-2-2−2i2i−2i2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ392-222-22-2-22-12i−2i2i−2i-221-12-2-11-212-2-11-11-1-11-1112i−2i−ii2i−2i−ii−i−iii−i−iii00000000000000003−33−3−i3i3−i3i300000000
χ402-222-22-2-22-12i−2i2i−2i-221-12-2-11-212-2-11-11-1-11-1112i−2i−ii2i−2i−ii−i−iii−i−iii0000000000000000−33−33i3−i3i3−i300000000
χ412-222-22-2-22-1−2i2i−2i2i-221-12-2-11-212-2-11-11-1-11-111−2i2ii−i−2i2ii−iii−i−iii−i−i00000000000000003−33−3i3−i3i3−i300000000
χ422-222-22-2-22-1−2i2i−2i2i-221-12-2-11-212-2-11-11-1-11-111−2i2ii−i−2i2ii−iii−i−iii−i−i0000000000000000−33−33−i3i3−i3i300000000
χ432-222-22-2-2-122i−2i2i−2i1-1-22-112-21-2-112-2-11-1-11-111−ii2i−2i−ii2i−2i−i−iii−i−iii00000000−i3i3−i3i33−33−30000000000000000
χ442-222-22-2-2-122i−2i2i−2i1-1-22-112-21-2-112-2-11-1-11-111−ii2i−2i−ii2i−2i−i−iii−i−iii00000000i3−i3i3−i3−33−330000000000000000
χ452-222-22-2-2-12−2i2i−2i2i1-1-22-112-21-2-112-2-11-1-11-111i−i−2i2ii−i−2i2iii−i−iii−i−i00000000−i3i3−i3i3−33−330000000000000000
χ462-222-22-2-2-12−2i2i−2i2i1-1-22-112-21-2-112-2-11-1-11-111i−i−2i2ii−i−2i2iii−i−iii−i−i00000000i3−i3i3−i33−33−30000000000000000
χ472-22-22-22-2222i−2i−2i2i-22-22-22-22-2-2-22-222-22-22-22-22i−2i2i−2i−2i2i−2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ482-22-22-22-222−2i2i2i−2i-22-22-22-22-2-2-22-222-22-22-22-2−2i2i−2i2i2i−2i2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ492-22-22-22-22-12i−2i−2i2i-221-1-221-1-21-221-1-11-11-11-112i−2i−ii−2i2ii−i−i−iiiii−i−i0000000000000000−i3i3i3−i3−333−300000000
χ502-22-22-22-22-12i−2i−2i2i-221-1-221-1-21-221-1-11-11-11-112i−2i−ii−2i2ii−i−i−iiiii−i−i0000000000000000i3−i3−i3i33−3−3300000000
χ512-22-22-22-22-1−2i2i2i−2i-221-1-221-1-21-221-1-11-11-11-11−2i2ii−i2i−2i−iiii−i−i−i−iii0000000000000000−i3i3i3−i33−3−3300000000
χ522-22-22-22-22-1−2i2i2i−2i-221-1-221-1-21-221-1-11-11-11-11−2i2ii−i2i−2i−iiii−i−i−i−iii0000000000000000i3−i3−i3i3−333−300000000
χ532-22-22-22-2-122i−2i−2i2i1-1-221-1-221-21-1-22-11-11-11-11−ii2i−2ii−i−2i2i−i−iiiii−i−i000000003−3−33i3−i3−i3i30000000000000000
χ542-22-22-22-2-122i−2i−2i2i1-1-221-1-221-21-1-22-11-11-11-11−ii2i−2ii−i−2i2i−i−iiiii−i−i00000000−333−3−i3i3i3−i30000000000000000
χ552-22-22-22-2-12−2i2i2i−2i1-1-221-1-221-21-1-22-11-11-11-11i−i−2i2i−ii2i−2iii−i−i−i−iii000000003−3−33−i3i3i3−i30000000000000000
χ562-22-22-22-2-12−2i2i2i−2i1-1-221-1-221-21-1-22-11-11-11-11i−i−2i2i−ii2i−2iii−i−i−i−iii00000000−333−3i3−i3−i3i30000000000000000
χ572-2-22-2-222220000-2-2-2-22-2-2222-222-22-2-22-2-22200000000000000000000000000000000000000002-22-20000
χ582-2-22-2-222220000-2-2-2-22-2-2222-222-22-2-22-2-2220000000000000000000000000000000000000000-22-220000
χ592-2-2-222-22220000-2-2-2-2-222-2222-2-222-2-2-222-2200000000000000000000000000000000000000002-2-220000
χ602-2-2-222-22220000-2-2-2-2-222-2222-2-222-2-2-222-220000000000000000000000000000000000000000-222-20000
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
χ63444-4-4-4-44-2-244-4-4-2-2-2-22222-2-22222111-1-1-1-11-2-2-2-222221111-1-1-1-100000000000000000000000000000000
χ64444-4-4-4-44-2-2-4-444-2-2-2-22222-2-22222111-1-1-1-112222-2-2-2-2-1-1-1-1111100000000000000000000000000000000
χ6544-444-4-4-44-200004-4-224422-42-4-4-2-2-2-22-2-2222000000000000000000000000000000000000000000000000
χ6644-444-4-4-4-240000-224-4-2-2-4-42-42244-2-22-2-2222000000000000000000000000000000000000000000000000
χ6744-444-4-4-4-2-20000-22-22-2-2222222-2-211-111-1-1-1000000003i−3i3i−3i3i−3i3i−3i00000000000000000000000000000000
χ6844-444-4-4-4-2-20000-22-22-2-2222222-2-211-111-1-1-100000000−3i3i−3i3i−3i3i−3i3i00000000000000000000000000000000
χ6944-4-4-444-44-200004-4-22-4-4-2-2-424422-2-2222-2-22000000000000000000000000000000000000000000000000
χ7044-4-4-444-4-240000-224-422442-4-2-2-4-4-2-2222-2-22000000000000000000000000000000000000000000000000
χ7144-4-4-444-4-2-20000-22-2222-2-222-2-22211-1-1-111-1000000003i−3i3i−3i−3i3i−3i3i00000000000000000000000000000000
χ7244-4-4-444-4-2-20000-22-2222-2-222-2-22211-1-1-111-100000000−3i3i−3i3i3i−3i3i−3i00000000000000000000000000000000
χ734-444-44-4-4-2-24i−4i4i−4i2-22-2-22-2222-22-221-111-11-1-1−2i2i−2i2i−2i2i−2i2iii−i−iii−i−i00000000000000000000000000000000
χ744-444-44-4-4-2-2−4i4i−4i4i2-22-2-22-2222-22-221-111-11-1-12i−2i2i−2i2i−2i2i−2i−i−iii−i−iii00000000000000000000000000000000
χ754-44-44-44-4-2-24i−4i−4i4i2-22-22-22-2222-22-21-11-11-11-1−2i2i−2i2i2i−2i2i−2iii−i−i−i−iii00000000000000000000000000000000
χ764-44-44-44-4-2-2−4i4i4i−4i2-22-22-22-2222-22-21-11-11-11-12i−2i2i−2i−2i2i−2i2i−i−iiiii−i−i00000000000000000000000000000000
χ774-4-44-4-4444-20000-4-4224-42-24-2-44-22-222-222-2-2000000000000000000000000000000000000000000000000
χ784-4-44-4-444-24000022-4-4-22-44-242-24-4-222-222-2-2000000000000000000000000000000000000000000000000
χ794-4-44-4-444-2-200002222-222-2-2-22-2-221-1-11-1-111000000003-3-333-3-3300000000000000000000000000000000
χ804-4-44-4-444-2-200002222-222-2-2-22-2-221-1-11-1-11100000000-333-3-333-300000000000000000000000000000000
χ814-4-4-444-444-20000-4-422-44-224-24-42-2-2222-2-22-2000000000000000000000000000000000000000000000000
χ824-4-4-444-44-24000022-4-42-24-4-24-22-44-2222-2-22-2000000000000000000000000000000000000000000000000
χ834-4-4-444-44-2-2000022222-2-22-2-2-222-21-1-1-111-11000000003-3-33-333-300000000000000000000000000000000
χ844-4-4-444-44-2-2000022222-2-22-2-2-222-21-1-1-111-1100000000-333-33-3-3300000000000000000000000000000000

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