Finite Group Databasebeta

← Group #13135221

Character table — Group #13135221

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order12222222223666666666663366666666666666366666666666666666666666444444444444121212121212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111-1-1-1-11111-1-1-1-111-1-11111111111-1-111-1-1111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111-1-1-1-11111-1-1-1-111-1-11111111111-1-111-1-1111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii
χ7111111-1-1-1-11111-1-1-1-111-1-11111111111-1-111-1-1111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ8111111-1-1-1-11111-1-1-1-111-1-11111111111-1-111-1-1111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i
χ911-1-11-11-11-111-1-111-1-11-11-1111111-1-1-1-1-1-1-1-11111-1111-1-1-1111-1-1-1-11111-1-1-1-1i−ii−ii−ii−i1-11-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ1011-1-11-11-11-111-1-111-1-11-11-1111111-1-1-1-1-1-1-1-11111-1111-1-1-1111-1-1-1-11111-1-1-1-1i−ii−i−ii−ii-11-11−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ1111-1-11-11-11-111-1-111-1-11-11-1111111-1-1-1-1-1-1-1-11111-1111-1-1-1111-1-1-1-11111-1-1-1-1−ii−iii−ii−i-11-11ii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ1211-1-11-11-11-111-1-111-1-11-11-1111111-1-1-1-1-1-1-1-11111-1111-1-1-1111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii1-11-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ1311-1-11-1-11-1111-1-1-1-1111-1-11111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111i−i−ii1-1-11−iii−i11-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i
χ1411-1-11-1-11-1111-1-1-1-1111-1-11111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111i−i−ii-111-1i−i−ii-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1511-1-11-1-11-1111-1-1-1-1111-1-11111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111−iii−i1-1-11i−i−ii11-1-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ1611-1-11-1-11-1111-1-1-1-1111-1-11111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111−iii−i-111-1−iii−i-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1722222222222222222222222-1222-122-1-1-1-122-1-1-1-1-122-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022220000000000000000-1-1-1-1-1-1-1-1
χ1822222222222222222222222-1222-122-1-1-1-122-1-1-1-1-122-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2000000000000000011111111
χ192222222222222222222222-12-1-1-12-1-12222-1-122-122-1-12-1-12-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000000000000-1-1-1-1-1-1-1-100000000
χ202222222222222222222222-12-1-1-12-1-12222-1-122-122-1-12-1-12-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000000000001111111100000000
χ21222222-2-2-2-22222-2-2-2-222-2-22-1222-122-1-1112211-1-1-1-2-21-2-21-1-1-1-1-1-1-111111111000000002i2i−2i−2i0000000000000000−i−i−i−iiiii
χ22222222-2-2-2-22222-2-2-2-222-2-22-1222-122-1-1112211-1-1-1-2-21-2-21-1-1-1-1-1-1-11111111100000000−2i−2i2i2i0000000000000000iiii−i−i−i−i
χ23222222-2-2-2-22222-2-2-2-222-2-2-12-1-1-12-1-122-2-2-1-1-2-2-12211-211-2-1-1-1-1-1-1-11111111122-2-20000000000000000-1-1-1-1111100000000
χ24222222-2-2-2-22222-2-2-2-222-2-2-12-1-1-12-1-122-2-2-1-1-2-2-12211-211-2-1-1-1-1-1-1-111111111-2-22200000000000000001111-1-1-1-100000000
χ252222-2-22-2-2222222222-2-2-2-2222-2-22-2-222-2-222-2-22-2-22-222-222-2-222-2-222-2-222-2-2000000000000000000000000000000000000
χ262222-2-22-2-2222222222-2-2-2-22-12-2-2-1-2-2-1-1112211-1112-2-12-2-1-111-1-111-1-111-1-11100000000000000000000000000003−33−33−33−3
χ272222-2-22-2-2222222222-2-2-2-22-12-2-2-1-2-2-1-1112211-1112-2-12-2-1-111-1-111-1-111-1-1110000000000000000000000000000−33−33−33−33
χ282222-2-22-2-2222222222-2-2-2-2-12-11121122-2-2-1-1-2-2-1-2-2-112-112-111-1-111-1-111-1-11100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ292222-2-22-2-2222222222-2-2-2-2-12-11121122-2-2-1-1-2-2-1-2-2-112-112-111-1-111-1-111-1-11100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ302222-2-2-222-22222-2-2-2-2-2-222222-2-22-2-2222222222-2-2-22-2-22-22-2-222-2-2-2-222-2-222000000000000000000000000000000000000
χ312222-2-2-222-22222-2-2-2-2-2-2222-12-2-2-1-2-2-1-1-1-122-1-1-111-221-221-111-1-11111-1-111-1-10000000000000000000000000000−i3i3−i3i3i3−i3i3−i3
χ322222-2-2-222-22222-2-2-2-2-2-2222-12-2-2-1-2-2-1-1-1-122-1-1-111-221-221-111-1-11111-1-111-1-10000000000000000000000000000i3−i3i3−i3−i3i3−i3i3
χ332222-2-2-222-22222-2-2-2-2-2-222-12-1112112222-1-122-1-2-21-1-21-1-2-111-1-11111-1-111-1-100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ342222-2-2-222-22222-2-2-2-2-2-222-12-1112112222-1-122-1-2-21-1-21-1-2-111-1-11111-1-111-1-100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ3522-2-22-22-22-222-2-222-2-22-22-22-1222-1-2-21111-2-2-1-1-1-1122-1-2-21-1-1-11111-1-1-1-11111000000002-22-20000000000000000-1-111-1-111
χ3622-2-22-22-22-222-2-222-2-22-22-22-1222-1-2-21111-2-2-1-1-1-1122-1-2-21-1-1-11111-1-1-1-1111100000000-22-22000000000000000011-1-111-1-1
χ3722-2-22-22-22-222-2-222-2-22-22-2-12-1-1-1211-2-2-2-21122-12-2-1-1211-2-1-1-11111-1-1-1-111112i−2i2i−2i0000000000000000−i−iii−i−iii00000000
χ3822-2-22-22-22-222-2-222-2-22-22-2-12-1-1-1211-2-2-2-21122-12-2-1-1211-2-1-1-11111-1-1-1-11111−2i2i−2i2i0000000000000000ii−i−iii−i−i00000000
χ3922-2-22-2-22-2222-2-2-2-2222-2-222-1222-1-2-211-1-1-2-211-1-11-2-2122-1-1-1-111111111-1-1-1-1000000002i−2i−2i2i0000000000000000−i−iiiii−i−i
χ4022-2-22-2-22-2222-2-2-2-2222-2-222-1222-1-2-211-1-1-2-211-1-11-2-2122-1-1-1-111111111-1-1-1-100000000−2i2i2i−2i0000000000000000ii−i−i−i−iii
χ4122-2-22-2-22-2222-2-2-2-2222-2-22-12-1-1-1211-2-22211-2-2-12-211-2-1-12-1-1-111111111-1-1-1-12i−2i−2i2i0000000000000000−i−iiiii−i−i00000000
χ4222-2-22-2-22-2222-2-2-2-2222-2-22-12-1-1-1211-2-22211-2-2-12-211-2-1-12-1-1-111111111-1-1-1-1−2i2i2i−2i0000000000000000ii−i−i−i−iii00000000
χ4322-2-2-2222-2-222-2-222-2-2-22-22222-2-2222-2-222-2-2-2-22-222-22-22-22-2-2-2-22222-2-2-2-222000000000000000000000000000000000000
χ4422-2-2-2222-2-222-2-222-2-2-22-222-12-2-2-12211-1-1-2-211-11-12-2-1-221-11111-1-1-1-11111-1-100000000000000000000000000003−3−333−3−33
χ4522-2-2-2222-2-222-2-222-2-2-22-222-12-2-2-12211-1-1-2-211-11-12-2-1-221-11111-1-1-1-11111-1-10000000000000000000000000000−333−3−333−3
χ4622-2-2-2222-2-222-2-222-2-2-22-22-12-1112-1-1-2-22211-2-2-1-22-1121-1-2-11111-1-1-1-11111-1-1000000000000000000003−3−333−3−3300000000
χ4722-2-2-2222-2-222-2-222-2-2-22-22-12-1112-1-1-2-22211-2-2-1-22-1121-1-2-11111-1-1-1-11111-1-100000000000000000000−333−3−333−300000000
χ4822-2-2-22-2-22222-2-2-2-222-222-2222-2-2222-2-2-2-2-2-2222-22-22-22-222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000
χ4922-2-2-22-2-22222-2-2-2-222-222-22-12-2-2-1221111-2-2-1-1-11-1-2212-2-1-11111-1-111-1-1-1-1110000000000000000000000000000−i3i3i3−i3i3−i3−i3i3
χ5022-2-2-22-2-22222-2-2-2-222-222-22-12-2-2-1221111-2-2-1-1-11-1-2212-2-1-11111-1-111-1-1-1-1110000000000000000000000000000i3−i3−i3i3−i3i3i3−i3
χ5122-2-2-22-2-22222-2-2-2-222-222-2-12-1112-1-1-2-2-2-21122-1-221-1-2-112-11111-1-111-1-1-1-111000000000000000000003−3−33−333−300000000
χ5222-2-2-22-2-22222-2-2-2-222-222-2-12-1112-1-1-2-2-2-21122-1-221-1-2-112-11111-1-111-1-1-1-11100000000000000000000−333−33−3−3300000000
χ534444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2111111111111111000000000000000000000000000000000000
χ54444444-4-4-4-44444-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-222-2-2221-2-22222221111111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ554444-4-44-4-4444444444-4-4-4-4-2-2-222-222-2-222-2-222122-22-2-22-21-1-111-1-111-1-111-1-1000000000000000000000000000000000000
χ564444-4-4-444-44444-4-4-4-4-4-444-2-2-222-222-2-2-2-2-2-2-2-21222-222-221-1-111-1-1-1-111-1-111000000000000000000000000000000000000
χ5744-4-44-44-44-444-4-444-4-44-44-4-2-2-2-2-2-222222222-2-21-22-2-2-2222111-1-1-1-11111-1-1-1-1000000000000000000000000000000000000
χ5844-4-44-4-44-4444-4-4-4-4444-4-44-2-2-2-2-2-22222-2-222221-22222-2-2-2111-1-1-1-1-1-1-1-11111000000000000000000000000000000000000
χ5944-4-4-4444-4-444-4-444-4-4-44-44-2-2-222-2-2-222-2-2222212-2-22-22-221-1-1-1-11111-1-1-1-111000000000000000000000000000000000000
χ6044-4-4-44-4-44444-4-4-4-444-444-4-2-2-222-2-2-2222222-2-212-22-22-22-21-1-1-1-111-1-11111-1-1000000000000000000000000000000000000
χ614-44-40000004-44-40000000044-400-4004-4004-400400000000-4004-40000000000000000000000000000000000000000000000
χ624-44-40000004-44-4000000004-2-400200-22−2i32i34-4−2i32i3-200000000200-220000−2i32i300−2i32i3000000000000000000000000000000000000
χ634-44-40000004-44-4000000004-2-400200-222i3−2i34-42i3−2i3-200000000200-2200002i3−2i3002i3−2i3000000000000000000000000000000000000
χ644-44-40000004-44-400000000-242−2i32i3-4−2i32i34-400-2200-2000000002−2i32i3-22−2i32i300000000000000000000000000000000000000000000
χ654-44-40000004-44-400000000-2422i3−2i3-42i3−2i34-400-2200-20000000022i3−2i3-222i3−2i300000000000000000000000000000000000000000000
χ664-44-40000004-44-400000000-2-22−2i32i32−2i32i3-22−2i32i3-22−2i32i3100000000-1i3−i31-1i3−i33-3i3−i33-3i3−i3000000000000000000000000000000000000
χ674-44-40000004-44-400000000-2-22−2i32i32−2i32i3-222i3−2i3-222i3−2i3100000000-1i3−i31-1i3−i3-33−i3i3-33−i3i3000000000000000000000000000000000000
χ684-44-40000004-44-400000000-2-222i3−2i322i3−2i3-22−2i32i3-22−2i32i3100000000-1−i3i31-1−i3i3-33i3−i3-33i3−i3000000000000000000000000000000000000
χ694-44-40000004-44-400000000-2-222i3−2i322i3−2i3-222i3−2i3-222i3−2i3100000000-1−i3i31-1−i3i33-3−i3i33-3−i3i3000000000000000000000000000000000000
χ704-4-440000004-4-440000000044-400-400-4400-4400400000000-400-440000000000000000000000000000000000000000000000
χ714-4-440000004-4-44000000004-2-4002002-2−2i32i3-442i3−2i3-2000000002002-200002i3−2i300−2i32i3000000000000000000000000000000000000
χ724-4-440000004-4-44000000004-2-4002002-22i3−2i3-44−2i32i3-2000000002002-20000−2i32i3002i3−2i3000000000000000000000000000000000000
χ734-4-440000004-4-4400000000-242−2i32i3-42i3−2i3-44002-200-2000000002−2i32i32-22i3−2i300000000000000000000000000000000000000000000
χ744-4-440000004-4-4400000000-2422i3−2i3-4−2i32i3-44002-200-20000000022i3−2i32-2−2i32i300000000000000000000000000000000000000000000
χ754-4-440000004-4-4400000000-2-22−2i32i322i3−2i32-2−2i32i32-22i3−2i3100000000-1i3−i3-11−i3i3-33−i3i33-3i3−i3000000000000000000000000000000000000
χ764-4-440000004-4-4400000000-2-22−2i32i322i3−2i32-22i3−2i32-2−2i32i3100000000-1i3−i3-11−i3i33-3i3−i3-33−i3i3000000000000000000000000000000000000
χ774-4-440000004-4-4400000000-2-222i3−2i32−2i32i32-2−2i32i32-22i3−2i3100000000-1−i3i3-11i3−i33-3−i3i3-33i3−i3000000000000000000000000000000000000
χ784-4-440000004-4-4400000000-2-222i3−2i32−2i32i32-22i3−2i32-2−2i32i3100000000-1−i3i3-11i3−i3-33i3−i33-3−i3i3000000000000000000000000000000000000
χ796666666666-3-3-3-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000000022220000-1-1-1-1-1-1-1-10000000000000000
χ806666666666-3-3-3-3-3-3-3-3-3-3-3-300000000000000000000000000000000000000000000-2-2-2-20000111111110000000000000000
χ81666666-6-6-6-6-3-3-3-33333-3-333000000000000000000000000000000000000000000002i2i−2i−2i0000−i−i−i−iiiii0000000000000000
χ82666666-6-6-6-6-3-3-3-33333-3-33300000000000000000000000000000000000000000000−2i−2i2i2i0000iiii−i−i−i−i0000000000000000
χ836666-6-66-6-66-3-3-3-3-3-3-3-333330000000000000000000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i30000000000000000
χ846666-6-66-6-66-3-3-3-3-3-3-3-333330000000000000000000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i30000000000000000
χ856666-6-6-666-6-3-3-3-3333333-3-300000000000000000000000000000000000000000000000000003−33−3−33−330000000000000000
χ866666-6-6-666-6-3-3-3-3333333-3-30000000000000000000000000000000000000000000000000000−33−333−33−30000000000000000
χ8766-6-66-66-66-6-3-333-3-333-33-33000000000000000000000000000000000000000000002i−2i2i−2i0000−i−iii−i−iii0000000000000000
χ8866-6-66-66-66-6-3-333-3-333-33-3300000000000000000000000000000000000000000000−2i2i−2i2i0000ii−i−iii−i−i0000000000000000
χ8966-6-66-6-66-66-3-33333-3-3-333-3000000000000000000000000000000000000000000002-2-220000-1-11111-1-10000000000000000
χ9066-6-66-6-66-66-3-33333-3-3-333-300000000000000000000000000000000000000000000-222-2000011-1-1-1-1110000000000000000
χ9166-6-6-6666-6-6-3-333-3-3333-33-300000000000000000000000000000000000000000000000000003−3−333−3−330000000000000000
χ9266-6-6-6666-6-6-3-333-3-3333-33-30000000000000000000000000000000000000000000000000000−333−3−333−30000000000000000
χ9366-6-6-66-6-666-3-33333-3-33-3-330000000000000000000000000000000000000000000000000000−i3i3i3−i3i3−i3−i3i30000000000000000
χ9466-6-6-66-6-666-3-33333-3-33-3-330000000000000000000000000000000000000000000000000000i3−i3−i3i3−i3i3i3−i30000000000000000
χ9512-1212-12000000-66-66−6i36i3−6i36i300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9612-1212-12000000-66-666i3−6i36i3−6i300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12-1212000000-666-6−6i36i36i3−6i300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-1212000000-666-66i3−6i3−6i36i300000000000000000000000000000000000000000000000000000000000000000000000000000000

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