Finite Group Databasebeta

← Group #10592553

Character table — Group #10592553

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222222222224444444444444444444444444444888888888888888881818363636363672
order1222333344666666666666448812121212121212122424242424242424242424242424242441212121212121212121212121212121244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1
χ4111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ51111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1
χ61111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11
χ71111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111-1-1-1-11
χ81111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-11111-1
χ922222222-2-22222222222220000-2-2-2-2-2-2-2-200000000000000000000000000000000022-200000
χ1022222222-2-22222222222220000-2-2-2-2-2-2-2-2000000000000000000000000000000000-2-2200000
χ1122222-1-1-1222-1-1-122-1-1-1-1-1-122222-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-100000000
χ1222222-1-1-1222-1-1-122-1-1-1-1-1-122-2-22-1-1-12-1-1-1-2-2-2-2111111111111-222-1-1-1-1-1-1-2-211111100000000
χ1322222-1-1-1222-1-1-122-1-1-1-1-1-1-2-2222-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2111111-2-211111100000000
χ1422222-1-1-1222-1-1-122-1-1-1-1-1-1-2-2-2-22-1-1-12-1-1-1-2-2-2-21111111111112-2-211111122-1-1-1-1-1-100000000
χ152222-12-1-122-12-1-1-1-122-1-1-1-12222-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-100000000
χ162222-12-1-122-12-1-1-1-122-1-1-1-122-2-2-12-1-1-12-1-11111-2-2-2-211111111-2-1-122-1-1-1-111-2-2111100000000
χ172222-12-1-122-12-1-1-1-122-1-1-1-1-2-222-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-211-2-2111111-2-2111100000000
χ182222-12-1-122-12-1-1-1-122-1-1-1-1-2-2-2-2-12-1-1-12-1-11111-2-2-2-211111111211-2-21111-1-122-1-1-1-100000000
χ192222-1-12-122-1-12-1-1-1-1-122-1-12222-1-12-1-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-100000000
χ202222-1-12-122-1-12-1-1-1-1-122-1-122-2-2-1-12-1-1-12-111111111-2-2-2-21111-2-1-1-1-122-1-11111-2-21100000000
χ212222-1-12-122-1-12-1-1-1-1-122-1-1-2-222-1-12-1-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-1-21111-2-2111111-2-21100000000
χ222222-1-12-122-1-12-1-1-1-1-122-1-1-2-2-2-2-1-12-1-1-12-111111111-2-2-2-2111121111-2-211-1-1-1-122-1-100000000
χ232222-1-1-1222-1-1-12-1-1-1-1-1-1222222-1-1-12-1-1-12-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-122-1-1-1-1-1-12200000000
χ242222-1-1-1222-1-1-12-1-1-1-1-1-12222-2-2-1-1-12-1-1-12111111111111-2-2-2-2-2-1-1-1-1-1-122111111-2-200000000
χ252222-1-1-1222-1-1-12-1-1-1-1-1-122-2-222-1-1-12-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-2111111-2-2111111-2-200000000
χ262222-1-1-1222-1-1-12-1-1-1-1-1-122-2-2-2-2-1-1-12-1-1-12111111111111-2-2-2-22111111-2-2-1-1-1-1-1-12200000000
χ272-22-222222-22222-2-2-2-2-2-2-2-200002222-2-2-2-20000000000000000000000000000000000002-2000
χ282-22-222222-22222-2-2-2-2-2-2-2-200002222-2-2-2-2000000000000000000000000000000000000-22000
χ292-22-22222-222222-2-2-2-2-2-2-2-22i−2i00-2-2-2-22222000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ302-22-22222-222222-2-2-2-2-2-2-2-2−2i2i00-2-2-2-2222200000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ312-22-22-1-1-1-222-1-1-1-2-21111112i−2i00-21112-1-1-10000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i302i−2i−ii−ii−ii003−33−33−300000000
χ322-22-22-1-1-1-222-1-1-1-2-21111112i−2i00-21112-1-1-10000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i302i−2i−ii−ii−ii00−33−33−3300000000
χ332-22-22-1-1-1-222-1-1-1-2-2111111−2i2i00-21112-1-1-10000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30−2i2ii−ii−ii−i00−33−33−3300000000
χ342-22-22-1-1-1-222-1-1-1-2-2111111−2i2i00-21112-1-1-10000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30−2i2ii−ii−ii−i003−33−33−300000000
χ352-22-2-12-1-1-22-12-1-111-2-211112i−2i001-211-12-1-1−i3−i3i3i30000−i3−i3i3i3i3i3−i3−i30−ii2i−2i−ii−ii3−3003−3−3300000000
χ362-22-2-12-1-1-22-12-1-111-2-211112i−2i001-211-12-1-1i3i3−i3−i30000i3i3−i3−i3−i3−i3i3i30−ii2i−2i−ii−ii−3300−333−300000000
χ372-22-2-12-1-1-22-12-1-111-2-21111−2i2i001-211-12-1-1−i3−i3i3i30000−i3−i3i3i3i3i3−i3−i30i−i−2i2ii−ii−i−3300−333−300000000
χ382-22-2-12-1-1-22-12-1-111-2-21111−2i2i001-211-12-1-1i3i3−i3−i30000i3i3−i3−i3−i3−i3i3i30i−i−2i2ii−ii−i3−3003−3−3300000000
χ392-22-2-1-12-1-22-1-12-11111-2-2112i−2i0011-21-1-12-1−i3−i3i3i3i3i3−i3−i30000−i3−i3i3i30−ii−ii2i−2i−ii3−3−33003−300000000
χ402-22-2-1-12-1-22-1-12-11111-2-2112i−2i0011-21-1-12-1i3i3−i3−i3−i3−i3i3i30000i3i3−i3−i30−ii−ii2i−2i−ii−333−300−3300000000
χ412-22-2-1-12-1-22-1-12-11111-2-211−2i2i0011-21-1-12-1−i3−i3i3i3i3i3−i3−i30000−i3−i3i3i30i−ii−i−2i2ii−i−333−300−3300000000
χ422-22-2-1-12-1-22-1-12-11111-2-211−2i2i0011-21-1-12-1i3i3−i3−i3−i3−i3i3i30000i3i3−i3−i30i−ii−i−2i2ii−i3−3−33003−300000000
χ432-22-2-1-1-12-22-1-1-12111111-2-22i−2i00111-2-1-1-12−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000−ii−ii−ii2i−2i3−33−3−330000000000
χ442-22-2-1-1-12-22-1-1-12111111-2-22i−2i00111-2-1-1-12i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000−ii−ii−ii2i−2i−33−333−30000000000
χ452-22-2-1-1-12-22-1-1-12111111-2-2−2i2i00111-2-1-1-12−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000i−ii−ii−i−2i2i−33−333−30000000000
χ462-22-2-1-1-12-22-1-1-12111111-2-2−2i2i00111-2-1-1-12i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000i−ii−ii−i−2i2i3−33−3−330000000000
χ472-2-22222200-2-2-2-22-22-22-22-200−i2i200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000002-2000−i2i20
χ482-2-22222200-2-2-2-22-22-22-22-200−i2i200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000000-22000i2−i20
χ492-2-22222200-2-2-2-22-22-22-22-200i2−i200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000002-2000i2−i20
χ502-2-22222200-2-2-2-22-22-22-22-200i2−i200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000000-22000−i2i20
χ5144444-2-2-2-4-44-2-2-244-2-2-2-2-2-20000-4222-422200000000000000000000000000000000000000000
χ524444-24-2-2-4-4-24-2-2-2-244-2-2-2-200002-4222-42200000000000000000000000000000000000000000
χ534444-2-24-2-4-4-2-24-2-2-2-2-244-2-2000022-4222-4200000000000000000000000000000000000000000
χ544444-2-2-24-4-4-2-2-24-2-2-2-2-2-2440000222-4222-400000000000000000000000000000000000000000
χ5544-4-4444400-4-4-4-4-44-44-44-4400000000000000000000000000000000000000000000000000000
χ5644-4-44-2-2-200-4222-442-22-22-200000000000000006−6−666−6−666−6−660000000000000000000000000
χ5744-4-44-2-2-200-4222-442-22-22-20000000000000000−666−6−666−6−666−60000000000000000000000000
χ5844-4-4-24-2-2002-4222-2-442-22-20000000000006−6−6600006−6−66−666−60000000000000000000000000
χ5944-4-4-24-2-2002-4222-2-442-22-2000000000000−666−60000−666−66−6−660000000000000000000000000
χ6044-4-4-2-24-20022-422-22-2-442-20000000000006−6−66−666−600006−6−660000000000000000000000000
χ6144-4-4-2-24-20022-422-22-2-442-2000000000000−666−66−6−660000−666−60000000000000000000000000
χ6244-4-4-2-2-2400222-42-22-22-2-440000000000006−6−666−6−66−666−600000000000000000000000000000
χ6344-4-4-2-2-2400222-42-22-22-2-44000000000000−666−6−666−66−6−6600000000000000000000000000000
χ644-44-44-2-2-24-44-2-2-2-4-422222200004-2-2-2-422200000000000000000000000000000000000000000
χ654-44-4-24-2-24-4-24-2-222-4-422220000-24-2-22-42200000000000000000000000000000000000000000
χ664-44-4-2-24-24-4-2-24-22222-4-4220000-2-24-222-4200000000000000000000000000000000000000000
χ674-44-4-2-2-244-4-2-2-24222222-4-40000-2-2-24222-400000000000000000000000000000000000000000
χ684-4-444-2-2-200-42224-4-22-22-2200−2i22i200000000−2i22i2−2i22i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000000000000
χ694-4-444-2-2-200-42224-4-22-22-22002i2−2i2000000002i2−2i22i2−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000000000000
χ704-4-44-24-2-2002-422-224-4-22-2200−2i22i200000000i2−i2i2−i2−2i22i2−2i22i2i2−i2i2−i2i2−i2i2−i20000000000000000000000000
χ714-4-44-24-2-2002-422-224-4-22-22002i2−2i200000000−i2i2−i2i22i2−2i22i2−2i2−i2i2−i2i2−i2i2−i2i20000000000000000000000000
χ724-4-44-2-24-20022-42-22-224-4-2200−2i22i200000000i2−i2i2−i2i2−i2i2−i2−2i22i2−2i22i2i2−i2i2−i20000000000000000000000000
χ734-4-44-2-24-20022-42-22-224-4-22002i2−2i200000000−i2i2−i2i2−i2i2−i2i22i2−2i22i2−2i2−i2i2−i2i20000000000000000000000000
χ744-4-44-2-2-2400222-4-22-22-224-400−2i22i200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−2i22i2−2i22i20000000000000000000000000
χ754-4-44-2-2-2400222-4-22-22-224-4002i2−2i200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22i2−2i22i2−2i20000000000000000000000000

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