Finite Group Databasebeta

← Group #10591334

Character table — Group #10591334

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
χ51111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ61111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ81111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ911-11-1-1-1111ii−i−i1111-1-1-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i1-1i−ii−i1-111-1-1ii−i−i11-1-1ii−i−iii−i−i11-1-1
χ1011-11-1-1-1111ii−i−i1111-1-1-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i1-1i−i−ii-1111-1-1ii−i−i-1-111−i−iii−i−iii-1-111
χ1111-11-1-1-1111ii−i−i1111-1-1-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-11−iii−i1-1-1-111−i−iii11-1-1ii−i−i−i−iii-1-111
χ1211-11-1-1-1111ii−i−i1111-1-1-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-11−ii−ii-11-1-111−i−iii-1-111−i−iiiii−i−i11-1-1
χ1311-11-1-1-1111−i−iii1111-1-1-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii1-1−iii−i-1111-1-1−i−iii-1-111ii−i−iii−i−i-1-111
χ1411-11-1-1-1111−i−iii1111-1-1-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii1-1−ii−ii1-111-1-1−i−iii11-1-1−i−iii−i−iii11-1-1
χ1511-11-1-1-1111−i−iii1111-1-1-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii-11i−ii−i-11-1-111ii−i−i-1-111ii−i−i−i−iii11-1-1
χ1611-11-1-1-1111−i−iii1111-1-1-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii-11i−i−ii1-1-1-111ii−i−i11-1-1−i−iiiii−i−i-1-111
χ17222222222-1222222-1-1222-1-1-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-10000000000000000
χ18222222222-1222222-1-1222-1-1-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-20000111111110000000000000000
χ19222222222-1-2-2-2-222-1-1222-1-1-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-21111111122-2-20000-1-1-1-111110000000000000000
χ20222222222-1-2-2-2-222-1-1222-1-1-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-211111111-2-22200001111-1-1-1-10000000000000000
χ2122222222-122222-1-122-1-1-1222-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-100000000
χ2222222222-122222-1-122-1-1-1222-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000001111111100000000
χ2322222222-12-2-2-2-2-1-122-1-1-1222-122-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000022-2-2000000001111-1-1-1-100000000
χ2422222222-12-2-2-2-2-1-122-1-1-1222-122-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000-2-22200000000-1-1-1-1111100000000
χ25222-2-2-22-22200002-22-222-222-2-2-2-2-222-2-222-2-200000000000000000000000000000000000000002-22-20000
χ26222-2-2-22-22200002-22-222-222-2-2-2-2-222-2-222-2-20000000000000000000000000000000000000000-22-220000
χ2722-22-2-2-222-12i2i−2i−2i22-1-1-2-2-21112-11-2-1-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii2-22i−2i0000-1-111−i−iii0000000000000000
χ2822-22-2-2-222-12i2i−2i−2i22-1-1-2-2-21112-11-2-1-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii-22−2i2i000011-1-1ii−i−i0000000000000000
χ2922-22-2-2-222-1−2i−2i2i2i22-1-1-2-2-21112-11-2-1-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i2-2−2i2i0000-1-111ii−i−i0000000000000000
χ3022-22-2-2-222-1−2i−2i2i2i22-1-1-2-2-21112-11-2-1-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i-222i−2i000011-1-1−i−iii0000000000000000
χ3122-22-2-2-22-122i2i−2i−2i-1-122111-2-2-2-12-21-1-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii00002i−2i2-200000000-1-111−i−iii00000000
χ3222-22-2-2-22-122i2i−2i−2i-1-122111-2-2-2-12-21-1-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii0000−2i2i-220000000011-1-1ii−i−i00000000
χ3322-22-2-2-22-12−2i−2i2i2i-1-122111-2-2-2-12-21-1-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i00002i−2i-220000000011-1-1−i−iii00000000
χ3422-22-2-2-22-12−2i−2i2i2i-1-122111-2-2-2-12-21-1-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i0000−2i2i2-200000000-1-111ii−i−i00000000
χ3522-2-222-2-22200002-22-2-2-22-2-22-2-22222-2-2-2-22200000000000000000000000000000000000000002i−2i−2i2i0000
χ3622-2-222-2-22200002-22-2-2-22-2-22-2-22222-2-2-2-2220000000000000000000000000000000000000000−2i2i2i−2i0000
χ372-222-22-2-2220000-22-2-22-2-22-22-22-222-22-22-2-22000000000000000000000000000000000000000000002i−2i2i−2i
χ382-222-22-2-2220000-22-2-22-2-22-22-22-222-22-22-2-2200000000000000000000000000000000000000000000−2i2i−2i2i
χ392-22-22-2-22222i−2i2i−2i-2-2-222-222-2-22-22-22-2-222-22-22i−2i2i−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ402-22-22-2-2222−2i2i−2i2i-2-2-222-222-2-22-22-22-2-222-22-2−2i2i−2i2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ412-22-22-2-222-12i−2i2i−2i-2-21-12-22-11121-1-2-111-1-11-11−ii−ii2i−2i2i−2i−i−iii−i−iii000000003−33−3−i3i3−i3i30000000000000000
χ422-22-22-2-222-12i−2i2i−2i-2-21-12-22-11121-1-2-111-1-11-11−ii−ii2i−2i2i−2i−i−iii−i−iii00000000−33−33i3−i3i3−i30000000000000000
χ432-22-22-2-222-1−2i2i−2i2i-2-21-12-22-11121-1-2-111-1-11-11i−ii−i−2i2i−2i2iii−i−iii−i−i000000003−33−3i3−i3i3−i30000000000000000
χ442-22-22-2-222-1−2i2i−2i2i-2-21-12-22-11121-1-2-111-1-11-11i−ii−i−2i2i−2i2iii−i−iii−i−i00000000−33−33−i3i3−i3i30000000000000000
χ452-22-22-2-22-122i−2i2i−2i11-22-11-12-2-2-1-221-111-1-11-112i−2i2i−2i−ii−ii−i−iii−i−iii0000000000000000−i3i3−i3i33−33−300000000
χ462-22-22-2-22-122i−2i2i−2i11-22-11-12-2-2-1-221-111-1-11-112i−2i2i−2i−ii−ii−i−iii−i−iii0000000000000000i3−i3i3−i3−33−3300000000
χ472-22-22-2-22-12−2i2i−2i2i11-22-11-12-2-2-1-221-111-1-11-11−2i2i−2i2ii−ii−iii−i−iii−i−i0000000000000000−i3i3−i3i3−33−3300000000
χ482-22-22-2-22-12−2i2i−2i2i11-22-11-12-2-2-1-221-111-1-11-11−2i2i−2i2ii−ii−iii−i−iii−i−i0000000000000000i3−i3i3−i33−33−300000000
χ492-2-222-22-2220000-22-2-2-222-22-2-222-22-22-2-222-2000000000000000000000000000000000000000000002i−2i−2i2i
χ502-2-222-22-2220000-22-2-2-222-22-2-222-22-22-2-222-200000000000000000000000000000000000000000000−2i2i2i−2i
χ512-2-2-2-2222222-2-22-2-2-22-22-2-2222-2-222-2-22-22-222-2-222-2-2222-2-2-2-22200000000000000000000000000000000
χ522-2-2-2-222222-222-2-2-2-22-22-2-2222-2-222-2-22-22-22-222-2-222-2-2-22222-2-200000000000000000000000000000000
χ532-2-2-2-22222-12-2-22-2-21-1-22-21-1-12112-111-11-11-1-111-12-2-22-1-11111-1-1000000003−3−33−333−30000000000000000
χ542-2-2-2-22222-12-2-22-2-21-1-22-21-1-12112-111-11-11-1-111-12-2-22-1-11111-1-100000000−333−33−3−330000000000000000
χ552-2-2-2-22222-1-222-2-2-21-1-22-21-1-12112-111-11-11-11-1-11-222-211-1-1-1-111000000003−3−333−3−330000000000000000
χ562-2-2-2-22222-1-222-2-2-21-1-22-21-1-12112-111-11-11-11-1-11-222-211-1-1-1-11100000000−333−3−333−30000000000000000
χ572-2-2-2-2222-122-2-2211-221-11-222-1-2-2-1-111-11-11-12-2-22-111-1-1-11111-1-10000000000000000−i3i3i3−i3−i3i3i3−i300000000
χ582-2-2-2-2222-122-2-2211-221-11-222-1-2-2-1-111-11-11-12-2-22-111-1-1-11111-1-10000000000000000i3−i3−i3i3i3−i3−i3i300000000
χ592-2-2-2-2222-12-222-211-221-11-222-1-2-2-1-111-11-11-1-222-21-1-1111-1-1-1-1110000000000000000−i3i3i3−i3i3−i3−i3i300000000
χ602-2-2-2-2222-12-222-211-221-11-222-1-2-2-1-111-11-11-1-222-21-1-1111-1-1-1-1110000000000000000i3−i3−i3i3−i3i3i3−i300000000
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
χ63444-4-4-44-44-200004-4-2244-4-2-22-422-4-2-222-2-222000000000000000000000000000000000000000000000000
χ64444-4-4-44-4-240000-224-4-2-2244-42-4-42-2-222-2-222000000000000000000000000000000000000000000000000
χ65444-4-4-44-4-2-20000-22-22-2-22-2-22222211-1-111-1-1000000003i−3i3i−3i3i−3i3i−3i00000000000000000000000000000000
χ66444-4-4-44-4-2-20000-22-22-2-22-2-22222211-1-111-1-100000000−3i3i−3i3i−3i3i−3i3i00000000000000000000000000000000
χ6744-44-4-4-44-2-24i4i−4i−4i-2-2-2-2222222-2-2221111-1-1-1-1−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i00000000000000000000000000000000
χ6844-44-4-4-44-2-2−4i−4i4i4i-2-2-2-2222222-2-2221111-1-1-1-12i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii00000000000000000000000000000000
χ6944-4-444-4-44-200004-4-22-4-4422-2-42-24-2-22222-2-2000000000000000000000000000000000000000000000000
χ7044-4-444-4-4-240000-224-422-2-4-442-44-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ7144-4-444-4-4-2-20000-22-2222-222-222-2-211-1-1-1-111000000003-33-3-33-3300000000000000000000000000000000
χ7244-4-444-4-4-2-20000-22-2222-222-222-2-211-1-1-1-11100000000-33-333-33-300000000000000000000000000000000
χ734-444-44-4-44-20000-44224-4-4-22-2-4-224-22-22-222-2000000000000000000000000000000000000000000000000
χ744-444-44-4-4-2400002-2-4-4-2224-4424-4-2-22-22-222-2000000000000000000000000000000000000000000000000
χ754-444-44-4-4-2-200002-222-222-22-22-22-21-11-11-1-11000000003-3-333-3-3300000000000000000000000000000000
χ764-444-44-4-4-2-200002-222-222-22-22-22-21-11-11-1-1100000000-333-3-333-300000000000000000000000000000000
χ774-44-44-4-44-2-24i−4i4i−4i222-2-22-2-222-22-221-1-111-11-1−2i2i−2i2i−2i2i−2i2iii−i−iii−i−i00000000000000000000000000000000
χ784-44-44-4-44-2-2−4i4i−4i4i222-2-22-2-222-22-221-1-111-11-12i−2i2i−2i2i−2i2i−2i−i−iii−i−iii00000000000000000000000000000000
χ794-4-444-44-44-20000-4422-4442-22-4-2-2-4-22-222-2-22000000000000000000000000000000000000000000000000
χ804-4-444-44-4-2400002-2-4-42-2-2-44-42442-22-222-2-22000000000000000000000000000000000000000000000000
χ814-4-444-44-4-2-200002-2222-2-22-222-2-221-11-1-111-1000000003i−3i−3i3i−3i3i3i−3i00000000000000000000000000000000
χ824-4-444-44-4-2-200002-2222-2-22-222-2-221-11-1-111-100000000−3i3i3i−3i3i−3i−3i3i00000000000000000000000000000000
χ834-4-4-4-4444-2-24-4-44222-22-222-2-2-222-21-1-11-11-11-222-2-222-211-1-1-1-11100000000000000000000000000000000
χ844-4-4-4-4444-2-2-444-4222-22-222-2-2-222-21-1-11-11-112-2-222-2-22-1-11111-1-100000000000000000000000000000000

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