Finite Group Databasebeta

← Group #11723720

Character table — Group #11723720

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222222222222244444444444444444444444444444444444444444444181818181818181818181818363636363636363636363636
order12222233366666666666663333366666666666666666666666666666666666666644441212121212121212244466121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111
χ51111-1-1111111-1-1-1-111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-1
χ61111-1-1111111-1-1-1-111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-111
χ71111-1-1111111-1-1-1-111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-11-111-1-1-1-111
χ81111-1-1111111-1-1-1-111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-11-1-11111-1-1
χ922222222-12222222-1-122-122-1-1-1-122-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002002-1-1-1-10000
χ1022222222-12222222-1-122-122-1-1-1-122-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-200-211110000
χ112222222-1222-1222222-1-122-12-1-1-1-1-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000002200000-1-1-1-1
χ122222222-1222-1222222-1-122-12-1-1-1-1-122-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000-2-2000001111
χ13222222-122-1-12-1-1-1-122222-1-1-12-1-12222-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ14222222-122-1-12-1-1-1-122222-1-1-12-1-12222-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ152222-2-222-1222-2-2-2-2-1-122-122-1-1-1-1-2-211222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111000000000000200-2-1-1110000
χ162222-2-222-1222-2-2-2-2-1-122-122-1-1-1-1-2-211222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111000000000000-200211-1-10000
χ172222-2-22-1222-1-2-2-2-222-1-122-12-1-1-111-2-2-1-1-1222-1-1-1-1-1-1-1-1-11111-2-2-2-211111111111100000000000002-200000-1-111
χ182222-2-22-1222-1-2-2-2-222-1-122-12-1-1-111-2-2-1-1-1222-1-1-1-1-1-1-1-1-11111-2-2-2-21111111111110000000000000-220000011-1-1
χ192222-2-2-122-1-12111122222-1-1-12-1-1-2-2-2-2-1-1-1-1-1-1222-1-1-1-1-1-111111111-2-2-2-21111111122-2-2-1-1-1-11111000000000000
χ202222-2-2-122-1-12111122222-1-1-12-1-1-2-2-2-2-1-1-1-1-1-1222-1-1-1-1-1-111111111-2-2-2-211111111-2-2221111-1-1-1-1000000000000
χ2122-2-2002222-2-200002-22-2-2-22222200002-2-22-2-22-2-222-2-2-2-200000000000000000000002i−2i00002i2i−2i−2i000000000000
χ2222-2-2002222-2-200002-22-2-2-22222200002-2-22-2-22-2-222-2-2-2-20000000000000000000000−2i2i0000−2i−2i2i2i000000000000
χ2322-2-200-122-11-2−i3−i3i3i32-22-2-21-1-12-1-10000-111-1112-2-2-1-11111−i3−i3i3i3−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i3002i−2i33−3−3−i−iii000000000000
χ2422-2-200-122-11-2−i3−i3i3i32-22-2-21-1-12-1-10000-111-1112-2-2-1-11111−i3−i3i3i3−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i300−2i2i−3−333ii−i−i000000000000
χ2522-2-200-122-11-2i3i3−i3−i32-22-2-21-1-12-1-10000-111-1112-2-2-1-11111i3i3−i3−i3i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i3002i−2i−3−333−i−iii000000000000
χ2622-2-200-122-11-2i3i3−i3−i32-22-2-21-1-12-1-10000-111-1112-2-2-1-11111i3i3−i3−i3i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i300−2i2i33−3−3ii−i−i000000000000
χ272-22-200222-22-20000-22-22-2-2222220000-22-2-22-2-22-2-2-222-2-2000000000000000000002i−2i002i−2i2i−2i0000000000000000
χ282-22-200222-22-20000-22-22-2-2222220000-22-2-22-2-22-2-2-222-2-200000000000000000000−2i2i00−2i2i−2i2i0000000000000000
χ292-22-200-1221-1-2−i3i3−i3i3-22-22-21-1-12-1-100001-111-11-22-211-1-111−i3i3−i3i3−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i32i−2i00−ii−ii3−33−3000000000000
χ302-22-200-1221-1-2−i3i3−i3i3-22-22-21-1-12-1-100001-111-11-22-211-1-111−i3i3−i3i3−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i3−2i2i00i−ii−i−33−33000000000000
χ312-22-200-1221-1-2i3−i3i3−i3-22-22-21-1-12-1-100001-111-11-22-211-1-111i3−i3i3−i3i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i32i−2i00−ii−ii−33−33000000000000
χ322-22-200-1221-1-2i3−i3i3−i3-22-22-21-1-12-1-100001-111-11-22-211-1-111i3−i3i3−i3i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i3−2i2i00i−ii−i3−33−3000000000000
χ332-2-222-2222-2-222-2-22-2-2-2-222222222-22-2-2-22-2-22-2-22-2-2-2-2222-2-222-2-2222-2-222-2-2-2-222000000000000000000000000
χ342-2-222-222-1-2-222-2-2211-2-2-122-1-1-1-12-2-11-2-2211-111-11111-1-12-2-22-111-1-1-111-1-11111-1-10000000000000000−i3i3−i3i30000
χ352-2-222-222-1-2-222-2-2211-2-2-122-1-1-1-12-2-11-2-2211-111-11111-1-12-2-22-111-1-1-111-1-11111-1-10000000000000000i3−i3i3−i30000
χ362-2-222-22-12-2-2-12-2-22-2-21122-12-1-1-1-112-211-1-2-2211-11111-1-1-111-12-2-22-1-111-1-11111-1-1000000000000000000003−33−3
χ372-2-222-22-12-2-2-12-2-22-2-21122-12-1-1-1-112-211-1-2-2211-11111-1-1-111-12-2-22-1-111-1-11111-1-100000000000000000000−33−33
χ382-2-222-2-122112-111-1-2-2-2-22-1-1-12-1-12-22-211-111-1-2-221111-1-1-111-1-111-122-2-2-1-11111-1-10000−i3i3i3−i3−i3i3i3−i3000000000000
χ392-2-222-2-122112-111-1-2-2-2-22-1-1-12-1-12-22-211-111-1-2-221111-1-1-111-1-111-122-2-2-1-11111-1-10000i3−i3−i3i3i3−i3−i3i3000000000000
χ402-2-22-22222-2-22-222-2-2-2-2-22222222-22-22-2-22-2-22-2-22-2-2-2-222-222-2-222-2-2-222-2-22222-2-2000000000000000000000000
χ412-2-22-2222-1-2-22-222-211-2-2-122-1-1-1-1-221-1-2-2211-111-11111-1-1-222-21-1-1111-1-111-1-1-1-1110000000000000000−i3i3i3−i30000
χ422-2-22-2222-1-2-22-222-211-2-2-122-1-1-1-1-221-1-2-2211-111-11111-1-1-222-21-1-1111-1-111-1-1-1-1110000000000000000i3−i3−i3i30000
χ432-2-22-222-12-2-2-1-222-2-2-21122-12-1-1-11-1-2211-1-2-2211-11111-1-11-1-11-222-211-1-111-1-1-1-111000000000000000000003−3−33
χ442-2-22-222-12-2-2-1-222-2-2-21122-12-1-1-11-1-2211-1-2-2211-11111-1-11-1-11-222-211-1-111-1-1-1-11100000000000000000000−333−3
χ452-2-22-22-1221121-1-11-2-2-2-22-1-1-12-1-1-22-2211-111-1-2-221111-1-11-1-111-1-11-2-22211-1-1-1-1110000−i3i3i3−i3i3−i3−i3i3000000000000
χ462-2-22-22-1221121-1-11-2-2-2-22-1-1-12-1-1-22-2211-111-1-2-221111-1-11-1-111-1-11-2-22211-1-1-1-1110000i3−i3−i3i3−i3i3i3−i3000000000000
χ474444444-2-244-24444-2-2-2-2-24-2-2111-2-2-2-2-2-2-2-2-2-2111111111-2-2-2-2-2-2-2-2111111111111000000000000000000000000
χ48444444-24-2-2-24-2-2-2-2-2-244-2-2-21-21144-2-2-2-2-2111-2-2-2111111-2-2-2-21111-2-2-2-211111111000000000000000000000000
χ49444444-2-24-2-2-2-2-2-2-244-2-24-21-2-211-2-244111-2-2-2-2-2-21111111111-2-2-2-2-2-2-2-211111111000000000000000000000000
χ50444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32-2-2-2-2111111111−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32111111111111−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000
χ51444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32-2-2-2-2111111111−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32111111111111−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000
χ524444-4-44-2-244-2-4-4-4-4-2-2-2-2-24-2-21112222-2-2-2-2-2-211111111122222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ534444-4-4-24-2-2-242222-2-244-2-2-21-211-4-422-2-2-2111-2-2-21111112222-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000000000000
χ544444-4-4-2-24-2-2-2222244-2-24-21-2-21122-4-4111-2-2-2-2-2-2111111-1-1-1-122222222-1-1-1-1-1-1-1-1000000000000000000000000
χ554444-4-4-2-2-2-2-2-22222-2-2-2-2-2-2111−1−3i32−1+3i322222111111111−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32-1-1-1-1-1-1-1-1-1-1-1-11+3i321−3i321+3i321−3i321+3i321−3i321+3i321−3i32000000000000000000000000
χ564444-4-4-2-2-2-2-2-22222-2-2-2-2-2-2111−1+3i32−1−3i322222111111111−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32-1-1-1-1-1-1-1-1-1-1-1-11−3i321+3i321−3i321+3i321−3i321+3i321−3i321+3i32000000000000000000000000
χ5744-4-40044-24-4-40000-224-42-44-2-2-2-200004-4-4-222-222-2-2222200000000000000000000000000000000000000000000
χ5844-4-4004-244-4200004-4-22-4-4-24-2-2-20000-2224-4-4-222-2-2222200000000000000000000000000000000000000000000
χ5944-4-4004-2-24-420000-22-222-4-2-21110000-222-2221-1-111-1-1-1-1000000003-33-33-33-3-33-33000000000000000000000000
χ6044-4-4004-2-24-420000-22-222-4-2-21110000-222-2221-1-111-1-1-1-100000000-33-33-33-333-33-3000000000000000000000000
χ6144-4-400-24-2-22-4−2i3−2i32i32i3-224-422-21-2110000-2221-1-1-22211-1-1-1-1−2i3−2i32i32i3i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i3000000000000000000000000
χ6244-4-400-24-2-22-42i32i3−2i3−2i3-224-422-21-2110000-2221-1-1-22211-1-1-1-12i32i3−2i3−2i3−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i3000000000000000000000000
χ6344-4-400-2-24-222−2i3−2i32i32i34-4-22-421-2-21100001-1-1-222-22211-1-1-1-1i3i3−i3−i3−2i3−2i32i32i30000i3i3i3i3−i3−i3−i3−i3000000000000000000000000
χ6444-4-400-2-24-2222i32i3−2i3−2i34-4-22-421-2-21100001-1-1-222-22211-1-1-1-1−i3−i3i3i32i32i3−2i3−2i30000−i3−i3−i3−i3i3i3i3i3000000000000000000000000
χ6544-4-400-2-2-2-222−2i3−2i32i32i3-22-2222111−1−3i32−1+3i3200001-1-11-1-11-1-1−1−3i32−1+3i321+3i321−3i321+3i321−3i32i3i3−i3−i3i3i3−i3−i33-33-3−3−i323−i32−3−i323−i323+i32−3+i323+i32−3+i32000000000000000000000000
χ6644-4-400-2-2-2-222−2i3−2i32i32i3-22-2222111−1+3i32−1−3i3200001-1-11-1-11-1-1−1+3i32−1−3i321−3i321+3i321−3i321+3i32i3i3−i3−i3i3i3−i3−i3-33-333−i32−3−i323−i32−3−i32−3+i323+i32−3+i323+i32000000000000000000000000
χ6744-4-400-2-2-2-2222i32i3−2i3−2i3-22-2222111−1−3i32−1+3i3200001-1-11-1-11-1-1−1−3i32−1+3i321+3i321−3i321+3i321−3i32−i3−i3i3i3−i3−i3i3i3-33-333+i32−3+i323+i32−3+i32−3−i323−i32−3−i323−i32000000000000000000000000
χ6844-4-400-2-2-2-2222i32i3−2i3−2i3-22-2222111−1+3i32−1−3i3200001-1-11-1-11-1-1−1+3i32−1−3i321−3i321+3i321−3i321+3i32−i3−i3i3i3−i3−i3i3i33-33-3−3+i323+i32−3+i323+i323−i32−3−i323−i32−3−i32000000000000000000000000
χ694-44-40044-2-44-400002-2-442-44-2-2-2-20000-44-42-222-2222-2-22200000000000000000000000000000000000000000000
χ704-44-4004-24-4420000-442-2-4-4-24-2-2-200002-22-44-42-2222-2-22200000000000000000000000000000000000000000000
χ714-44-4004-2-2-44200002-22-22-4-2-211100002-222-22-11-1-1-111-1-1000000003-3-333-3-333-3-33000000000000000000000000
χ724-44-4004-2-2-44200002-22-22-4-2-211100002-222-22-11-1-1-111-1-100000000-333-3-333-3-333-3000000000000000000000000
χ734-44-400-24-22-2-4−2i32i3−2i32i32-2-4422-21-21100002-22-11-12-22-1-111-1-1−2i32i3−2i32i3i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ744-44-400-24-22-2-42i3−2i32i3−2i32-2-4422-21-21100002-22-11-12-22-1-111-1-12i3−2i32i3−2i3−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ754-44-400-2-242-22−2i32i3−2i32i3-442-2-421-2-2110000-11-12-222-22-1-111-1-1i3−i3i3−i3−2i32i3−2i32i30000i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ764-44-400-2-242-222i3−2i32i3−2i3-442-2-421-2-2110000-11-12-222-22-1-111-1-1−i3i3−i3i32i3−2i32i3−2i30000−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ774-44-400-2-2-22-22−2i32i3−2i32i32-22-222111−1−3i32−1+3i320000-11-1-11-1-11-11+3i321−3i32−1−3i32−1+3i321+3i321−3i32i3−i3i3−i3i3−i3i3−i33-3-33−3−i323−i323+i32−3+i32−3−i323−i323+i32−3+i32000000000000000000000000
χ784-44-400-2-2-22-22−2i32i3−2i32i32-22-222111−1+3i32−1−3i320000-11-1-11-1-11-11−3i321+3i32−1+3i32−1−3i321−3i321+3i32i3−i3i3−i3i3−i3i3−i3-333-33−i32−3−i32−3+i323+i323−i32−3−i32−3+i323+i32000000000000000000000000
χ794-44-400-2-2-22-222i3−2i32i3−2i32-22-222111−1−3i32−1+3i320000-11-1-11-1-11-11+3i321−3i32−1−3i32−1+3i321+3i321−3i32−i3i3−i3i3−i3i3−i3i3-333-33+i32−3+i32−3−i323−i323+i32−3+i32−3−i323−i32000000000000000000000000
χ804-44-400-2-2-22-222i3−2i32i3−2i32-22-222111−1+3i32−1−3i320000-11-1-11-1-11-11−3i321+3i32−1+3i32−1−3i321−3i321+3i32−i3i3−i3i3−i3i3−i3i33-3-33−3+i323+i323−i32−3−i32−3+i323+i323−i32−3−i32000000000000000000000000
χ814-4-444-44-2-2-4-4-24-4-442222-24-2-2111-22-2222-222-2-1-11-1-1-1-111-222-2-222-211-1-111-1-1-1-111000000000000000000000000
χ824-4-444-4-24-2224-222-222-4-4-2-2-21-2114-4-2222-2-1-1122-2-1-1-1-111-222-21-1-11-2-22211-1-1-1-111000000000000000000000000
χ834-4-444-4-2-2422-2-222-2-4-4224-21-2-211-224-4-1-1122-222-2-1-1-1-1111-1-11-222-2-2-22211-1-1-1-111000000000000000000000000
χ844-4-444-4-2-2-222-2-222-22222-2-2111−1−3i32−1+3i32-22-22-1-11-1-11-1-111+3i321−3i321+3i321−3i32−1−3i32−1+3i321-1-111-1-1111-1-1−1−3i32−1+3i321+3i321−3i321+3i321−3i32−1−3i32−1+3i32000000000000000000000000
χ854-4-444-4-2-2-222-2-222-22222-2-2111−1+3i32−1−3i32-22-22-1-11-1-11-1-111−3i321+3i321−3i321+3i32−1+3i32−1−3i321-1-111-1-1111-1-1−1+3i32−1−3i321−3i321+3i321−3i321+3i32−1+3i32−1−3i32000000000000000000000000
χ864-4-44-444-2-2-4-4-2-444-42222-24-2-21112-22-222-222-2-1-11-1-1-1-1112-2-222-2-22-1-111-1-11111-1-1000000000000000000000000
χ874-4-44-44-24-22242-2-2222-4-4-2-2-21-211-442-222-2-1-1122-2-1-1-1-1112-2-22-111-122-2-2-1-11111-1-1000000000000000000000000
χ884-4-44-44-2-2422-22-2-22-4-4224-21-2-2112-2-44-1-1122-222-2-1-1-1-111-111-12-2-2222-2-2-1-11111-1-1000000000000000000000000
χ894-4-44-44-2-2-222-22-2-222222-2-2111−1−3i32−1+3i322-22-2-1-11-1-11-1-111+3i321−3i321+3i321−3i32−1−3i32−1+3i32-111-1-111-1-1-1111+3i321−3i32−1−3i32−1+3i32−1−3i32−1+3i321+3i321−3i32000000000000000000000000
χ904-4-44-44-2-2-222-22-2-222222-2-2111−1+3i32−1−3i322-22-2-1-11-1-11-1-111−3i321+3i321−3i321+3i32−1+3i32−1−3i32-111-1-111-1-1-1111−3i321+3i32−1+3i32−1−3i32−1+3i32−1−3i321−3i321+3i32000000000000000000000000

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