Finite Group Databasebeta

← Group #10592486

Character table — Group #10592486

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222222222224444444444444444444444444444888888888888888881818363636363672
order12223333446666666666664488121212121212121224242424242424242424242424242424266666666121212121212121244224884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1
χ4111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111
χ51111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1
χ61111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11
χ71111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-11-1-11
χ81111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-111-1
χ922222222-2-22222222222220000-2-2-2-2-2-2-2-20000000000000000000000000000000002200-2000
χ1022222222-2-22222222222220000-2-2-2-2-2-2-2-2000000000000000000000000000000000-2-2002000
χ1122222-1-1-1222-1-1-12-1-1-12-1-1-122222-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-100000000
χ1222222-1-1-1222-1-1-12-1-1-12-1-1-122-2-22-1-1-12-1-1-1-2-2-2-2111111111111-2-2-211111122-1-1-1-1-1-100000000
χ1322222-1-1-1222-1-1-12-1-1-12-1-1-1-2-2222-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2111111-2-211111100000000
χ1422222-1-1-1222-1-1-12-1-1-12-1-1-1-2-2-2-22-1-1-12-1-1-1-2-2-2-2111111111111222-1-1-1-1-1-1-2-211111100000000
χ152222-12-1-122-12-1-1-12-1-1-12-1-12222-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-100000000
χ162222-12-1-122-12-1-1-12-1-1-12-1-122-2-2-12-1-1-12-1-11111-2-2-2-211111111-211-2-21111-1-122-1-1-1-100000000
χ172222-12-1-122-12-1-1-12-1-1-12-1-1-2-222-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-211-2-2111111-2-2111100000000
χ182222-12-1-122-12-1-1-12-1-1-12-1-1-2-2-2-2-12-1-1-12-1-11111-2-2-2-2111111112-1-122-1-1-1-111-2-2111100000000
χ192222-1-12-122-1-12-1-1-12-1-1-12-12222-1-12-1-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-100000000
χ202222-1-12-122-1-12-1-1-12-1-1-12-122-2-2-1-12-1-1-12-111111111-2-2-2-21111-21111-2-211-1-1-1-122-1-100000000
χ212222-1-12-122-1-12-1-1-12-1-1-12-1-2-222-1-12-1-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-1-21111-2-2111111-2-21100000000
χ222222-1-12-122-1-12-1-1-12-1-1-12-1-2-2-2-2-1-12-1-1-12-111111111-2-2-2-211112-1-1-1-122-1-11111-2-21100000000
χ232222-1-1-1222-1-1-12-1-1-12-1-1-122222-1-1-12-1-1-12-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-122-1-1-1-1-1-12200000000
χ242222-1-1-1222-1-1-12-1-1-12-1-1-1222-2-2-1-1-12-1-1-12111111111111-2-2-2-2-2111111-2-2-1-1-1-1-1-12200000000
χ252222-1-1-1222-1-1-12-1-1-12-1-1-12-2-222-1-1-12-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-2111111-2-2111111-2-200000000
χ262222-1-1-1222-1-1-12-1-1-12-1-1-12-2-2-2-2-1-1-12-1-1-12111111111111-2-2-2-22-1-1-1-1-1-122111111-2-200000000
χ2722-2-22222002222-2-2-2-2-2-2-2-200−i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000002i−2i0002−20
χ2822-2-22222002222-2-2-2-2-2-2-2-200−i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000−2i2i000−220
χ2922-2-22222002222-2-2-2-2-2-2-2-200i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000002i−2i000−220
χ3022-2-22222002222-2-2-2-2-2-2-2-200i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000−2i2i0002−20
χ312-2-2222222-2-2-2-2-22222-2-2-2-22i−2i002222-2-2-2-200000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ322-2-2222222-2-2-2-2-22222-2-2-2-2−2i2i002222-2-2-2-20000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ332-2-222222-22-2-2-2-22222-2-2-2-20000-2-2-2-22222000000000000000000000000000000000002-20000
χ342-2-222222-22-2-2-2-22222-2-2-2-20000-2-2-2-2222200000000000000000000000000000000000-220000
χ352-2-222-1-1-12-2-21112-1-1-1-21112i−2i002-1-1-1-211100003−33−33−33−33−33−3000−i3i3−i3i3−i3i32i−2i−ii−ii−ii00000000
χ362-2-222-1-1-12-2-21112-1-1-1-21112i−2i002-1-1-1-21110000−33−33−33−33−33−33000i3−i3i3−i3i3−i32i−2i−ii−ii−ii00000000
χ372-2-222-1-1-12-2-21112-1-1-1-2111−2i2i002-1-1-1-211100003−33−33−33−33−33−3000i3−i3i3−i3i3−i3−2i2ii−ii−ii−i00000000
χ382-2-222-1-1-12-2-21112-1-1-1-2111−2i2i002-1-1-1-21110000−33−33−33−33−33−33000−i3i3−i3i3−i3i3−2i2ii−ii−ii−i00000000
χ392-2-22-12-1-12-21-211-12-1-11-2112i−2i00-12-1-11-2113−33−300003−33−3−33−330−i3i300−i3i3i3−i3−ii2i−2i−ii−ii00000000
χ402-2-22-12-1-12-21-211-12-1-11-2112i−2i00-12-1-11-211−33−330000−33−333−33−30i3−i300i3−i3−i3i3−ii2i−2i−ii−ii00000000
χ412-2-22-12-1-12-21-211-12-1-11-211−2i2i00-12-1-11-2113−33−300003−33−3−33−330i3−i300i3−i3−i3i3i−i−2i2ii−ii−i00000000
χ422-2-22-12-1-12-21-211-12-1-11-211−2i2i00-12-1-11-211−33−330000−33−333−33−30−i3i300−i3i3i3−i3i−i−2i2ii−ii−i00000000
χ432-2-22-1-12-12-211-21-1-12-111-212i−2i00-1-12-111-213−33−3−33−3300003−33−30−i3i3i3−i300−i3i3−ii−ii2i−2i−ii00000000
χ442-2-22-1-12-12-211-21-1-12-111-212i−2i00-1-12-111-21−33−333−33−30000−33−330i3−i3−i3i300i3−i3−ii−ii2i−2i−ii00000000
χ452-2-22-1-12-12-211-21-1-12-111-21−2i2i00-1-12-111-213−33−3−33−3300003−33−30i3−i3−i3i300i3−i3i−ii−i−2i2ii−i00000000
χ462-2-22-1-12-12-211-21-1-12-111-21−2i2i00-1-12-111-21−33−333−33−30000−33−330−i3i3i3−i300−i3i3i−ii−i−2i2ii−i00000000
χ472-2-22-1-1-122-2111-2-1-1-12111-22i−2i00-1-1-12111-23−33−33−33−3−33−3300000−i3i3−i3i3i3−i300−ii−ii−ii2i−2i00000000
χ482-2-22-1-1-122-2111-2-1-1-12111-22i−2i00-1-1-12111-2−33−33−33−333−33−300000i3−i3i3−i3−i3i300−ii−ii−ii2i−2i00000000
χ492-2-22-1-1-122-2111-2-1-1-12111-2−2i2i00-1-1-12111-23−33−33−33−3−33−3300000i3−i3i3−i3−i3i300i−ii−ii−i−2i2i00000000
χ502-2-22-1-1-122-2111-2-1-1-12111-2−2i2i00-1-1-12111-2−33−33−33−333−33−300000−i3i3−i3i3i3−i300i−ii−ii−i−2i2i00000000
χ5144444-2-2-2-4-44-2-2-24-2-2-24-2-2-20000-4222-422200000000000000000000000000000000000000000
χ524444-24-2-2-4-4-24-2-2-24-2-2-24-2-200002-4222-42200000000000000000000000000000000000000000
χ534444-2-24-2-4-4-2-24-2-2-24-2-2-24-2000022-4222-4200000000000000000000000000000000000000000
χ544444-2-2-24-4-4-2-2-24-2-2-24-2-2-240000222-4222-400000000000000000000000000000000000000000
χ5544-4-44-2-2-2004-2-2-2-4222-422200−2i22i200000000−2i2−2i22i22i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000000000000
χ5644-4-44-2-2-2004-2-2-2-4222-4222002i2−2i2000000002i22i2−2i2−2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000000000000
χ5744-4-4-24-2-200-24-2-22-4222-42200−2i22i200000000i2i2−i2−i2−2i2−2i22i22i2i2i2−i2−i2i2i2−i2−i20000000000000000000000000
χ5844-4-4-24-2-200-24-2-22-4222-422002i2−2i200000000−i2−i2i2i22i22i2−2i2−2i2−i2−i2i2i2−i2−i2i2i20000000000000000000000000
χ5944-4-4-2-24-200-2-24-222-4222-4200−2i22i200000000i2i2−i2−i2i2i2−i2−i2−2i2−2i22i22i2i2i2−i2−i20000000000000000000000000
χ6044-4-4-2-24-200-2-24-222-4222-42002i2−2i200000000−i2−i2i2i2−i2−i2i2i22i22i2−2i2−2i2−i2−i2i2i20000000000000000000000000
χ6144-4-4-2-2-2400-2-2-24222-4222-400−2i22i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−2i2−2i22i22i20000000000000000000000000
χ6244-4-4-2-2-2400-2-2-24222-4222-4002i2−2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22i22i2−2i2−2i20000000000000000000000000
χ634-44-4444400-4-4-4-4-4-4-4-4444400000000000000000000000000000000000000000000000000000
χ644-44-44-2-2-200-4222-42224-2-2-20000000000000000i6−i6−i6i6i6−i6−i6i6i6−i6−i6i60000000000000000000000000
χ654-44-44-2-2-200-4222-42224-2-2-20000000000000000−i6i6i6−i6−i6i6i6−i6−i6i6i6−i60000000000000000000000000
χ664-44-4-24-2-2002-4222-422-24-2-2000000000000i6−i6−i6i60000i6−i6−i6i6−i6i6i6−i60000000000000000000000000
χ674-44-4-24-2-2002-4222-422-24-2-2000000000000−i6i6i6−i60000−i6i6i6−i6i6−i6−i6i60000000000000000000000000
χ684-44-4-2-24-20022-4222-42-2-24-2000000000000i6−i6−i6i6−i6i6i6−i60000i6−i6−i6i60000000000000000000000000
χ694-44-4-2-24-20022-4222-42-2-24-2000000000000−i6i6i6−i6i6−i6−i6i60000−i6i6i6−i60000000000000000000000000
χ704-44-4-2-2-2400222-4222-4-2-2-24000000000000i6−i6−i6i6i6−i6−i6i6−i6i6i6−i600000000000000000000000000000
χ714-44-4-2-2-2400222-4222-4-2-2-24000000000000−i6i6i6−i6−i6i6i6−i6i6−i6−i6i600000000000000000000000000000
χ724-4-444-2-2-2-44-42224-2-2-2-42220000-42224-2-2-200000000000000000000000000000000000000000
χ734-4-44-24-2-2-442-422-24-2-22-42200002-422-24-2-200000000000000000000000000000000000000000
χ744-4-44-2-24-2-4422-42-2-24-222-42000022-42-2-24-200000000000000000000000000000000000000000
χ754-4-44-2-2-24-44222-4-2-2-24222-40000222-4-2-2-2400000000000000000000000000000000000000000

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