Finite Group Databasebeta

← Group #13139936

Character table — Group #13139936

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order12222234444666666612121212336666661212121212121212366666666666121212121212121212121212444444448888121212121212121212121212121212122424242424242424
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
χ51111-1-111-1-111-1-1-1-11111-1-11111111111-1-1-1-1111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111-1-111-1-111-1-1-1-11111-1-11111111111-1-1-1-1111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ71111-1-111-1-111-1-1-1-11111-1-11111111111-1-1-1-1111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ81111-1-111-1-111-1-1-1-11111-1-11111111111-1-1-1-1111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911-1-11-11-11-11-111-1-11-11-11-111-1-111-1-1-1-111-1-111111-1-1-1-111-1-111-11-111-1-111-1-1i−ii−ii−ii−i1-11-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ1011-1-11-11-11-11-111-1-11-11-11-111-1-111-1-1-1-111-1-111111-1-1-1-111-1-111-11-111-1-111-1-1i−ii−i−ii−ii-11-11−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ1111-1-11-11-11-11-111-1-11-11-11-111-1-111-1-1-1-111-1-111111-1-1-1-111-1-111-11-111-1-111-1-1−ii−iii−ii−i-11-11ii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ1211-1-11-11-11-11-111-1-11-11-11-111-1-111-1-1-1-111-1-111111-1-1-1-111-1-111-11-111-1-111-1-1−ii−ii−ii−ii1-11-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ1311-1-1-111-1-111-1-1-1111-11-1-1111-1-111-1-1-1-1-1-111111-1-111-1-1-1-11111-1-1111-1-1-1-111i−i−iii−i−ii1-1-11ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ1411-1-1-111-1-111-1-1-1111-11-1-1111-1-111-1-1-1-1-1-111111-1-111-1-1-1-11111-1-1111-1-1-1-111i−i−ii−iii−i-111-1−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ1511-1-1-111-1-111-1-1-1111-11-1-1111-1-111-1-1-1-1-1-111111-1-111-1-1-1-11111-1-1111-1-1-1-111−iii−ii−i−ii-111-1ii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ1611-1-1-111-1-111-1-1-1111-11-1-1111-1-111-1-1-1-1-1-111111-1-111-1-1-1-11111-1-1111-1-1-1-111−iii−i−iii−i1-1-11−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
χ1722222222222222222222222-1222-1-1-122-1-1-1-122-12-12-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122220000000000000000-1-1-1-1-1-1-1-100000000
χ1822222222222222222222222-1222-1-1-122-1-1-1-122-12-12-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-200000000000000001111111100000000
χ192222222222222222222222-12-1-1-1222-1-12222-1-1-1-12-12-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000000022220000000000000000-1-1-1-1-1-1-1-1
χ202222222222222222222222-12-1-1-1222-1-12222-1-1-1-12-12-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2000000000000000011111111
χ212222222-2-2-2-22222222-2-2-2-222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ222222222-2-2-2-22222222-2-2-2-22-1222-1-1-1-2-21111-2-2-12-12-1-1-1-1-1-1-1-111-2-21111111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ232222222-2-2-2-22222222-2-2-2-22-1222-1-1-1-2-21111-2-2-12-12-1-1-1-1-1-1-1-111-2-21111111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ242222222-2-2-2-22222222-2-2-2-2-12-1-1-122211-2-2-2-211-1-12-12-1-1-1-1-1-1-1-2-2111111111100000000000000000000000000003−33−33−33−3
χ252222222-2-2-2-22222222-2-2-2-2-12-1-1-122211-2-2-2-211-1-12-12-1-1-1-1-1-1-1-2-211111111110000000000000000000000000000−33−33−33−33
χ262222-2-222-2-222-2-2-2-22222-2-22-1222-1-1-122111122-1-21-21-1-11111-1-1-1-2-2-1-1-1-1111122-2-20000000000000000-1-1-1-1111100000000
χ272222-2-222-2-222-2-2-2-22222-2-22-1222-1-1-122111122-1-21-21-1-11111-1-1-1-2-2-1-1-1-11111-2-22200000000000000001111-1-1-1-100000000
χ282222-2-222-2-222-2-2-2-22222-2-2-12-1-1-1222-1-1-2-2-2-2-1-1-11-21-2-1-11111-12211-1-1-1-111110000000022-2-20000000000000000-1-1-1-11111
χ292222-2-222-2-222-2-2-2-22222-2-2-12-1-1-1222-1-1-2-2-2-2-1-1-11-21-2-1-11111-12211-1-1-1-1111100000000-2-22200000000000000001111-1-1-1-1
χ302222-2-22-222-22-2-2-2-222-2-22222222222-2-22222-2-22-2-2-2-222-2-2-2-22-2-222-2-2-2-22222000000000000000000000000000000000000
χ312222-2-22-222-22-2-2-2-222-2-2222-1222-1-1-1-2-2-1-1-1-1-2-2-1-21-21-1-11111-111221111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ322222-2-22-222-22-2-2-2-222-2-2222-1222-1-1-1-2-2-1-1-1-1-2-2-1-21-21-1-11111-111221111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ332222-2-22-222-22-2-2-2-222-2-222-12-1-1-122211222211-11-21-2-1-11111-1-2-2-1-11111-1-1-1-100000000000000000000000000003−33−3−33−33
χ342222-2-22-222-22-2-2-2-222-2-222-12-1-1-122211222211-11-21-2-1-11111-1-2-2-1-11111-1-1-1-10000000000000000000000000000−33−333−33−3
χ3522-2-22-222-22-2-222-2-22-2-22-2222-2-222-2-222-2-222-2-2222-2-2-2-222-2-22-22-22-2-222-2-222000000000000000000000000000000000000
χ3622-2-22-222-22-2-222-2-22-2-22-222-1-2-22-1112211-1-1-2-2-12-1-2111-1-111-11-1-2211-1-111-1-1000000000000000000003−3−333−3−3300000000
χ3722-2-22-222-22-2-222-2-22-2-22-222-1-2-22-1112211-1-1-2-2-12-1-2111-1-111-11-1-2211-1-111-1-100000000000000000000−333−3−333−300000000
χ3822-2-22-222-22-2-222-2-22-2-22-22-1211-12-2-2-1-1-2-22211-1-121-211-1-111-1-221-111-1-111-1-100000000000000000000000000003−3−333−3−33
χ3922-2-22-222-22-2-222-2-22-2-22-22-1211-12-2-2-1-1-2-22211-1-121-211-1-111-1-221-111-1-111-1-10000000000000000000000000000−333−3−333−3
χ4022-2-22-22-22-22-222-2-22-22-22-22-1-2-22-111-2-2-1-11122-12-1-2111-1-111-1-112-2-1-111-1-1112i−2i2i−2i0000000000000000−i−iii−i−iii00000000
χ4122-2-22-22-22-22-222-2-22-22-22-22-1-2-22-111-2-2-1-11122-12-1-2111-1-111-1-112-2-1-111-1-111−2i2i−2i2i0000000000000000ii−i−iii−i−i00000000
χ4222-2-22-22-22-22-222-2-22-22-22-2-1211-12-2-21122-2-2-1-1-1-121-211-1-111-12-2-11-1-111-1-111000000002-22-20000000000000000-1-111-1-111
χ4322-2-22-22-22-22-222-2-22-22-22-2-1211-12-2-21122-2-2-1-1-1-121-211-1-111-12-2-11-1-111-1-11100000000-22-22000000000000000011-1-111-1-1
χ4422-2-2-22222-2-2-2-2-2222-2-222-222-2-222-2-22222-2-2-2-22-2-222-2-2-2-2222-222-2-2-22222-2-2000000000000000000000000000000000000
χ4522-2-2-22222-2-2-2-2-2222-2-222-22-1-2-22-11122-1-111-2-2-1-212-11111-1-1-11-12-211-1-1-1-111000000000000000000003−3−33−333−300000000
χ4622-2-2-22222-2-2-2-2-2222-2-222-22-1-2-22-11122-1-111-2-2-1-212-11111-1-1-11-12-211-1-1-1-11100000000000000000000−333−33−3−3300000000
χ4722-2-2-22222-2-2-2-2-2222-2-222-2-1211-12-2-2-1-122-2-211-11-2-121111-1-1-1-22-1111-1-1-1-11100000000000000000000000000003−3−33−333−3
χ4822-2-2-22222-2-2-2-2-2222-2-222-2-1211-12-2-2-1-122-2-211-11-2-121111-1-1-1-22-1111-1-1-1-1110000000000000000000000000000−333−33−3−33
χ4922-2-2-222-2-222-2-2-2222-22-2-222-1-2-22-111-2-211-1-122-1-212-11111-1-1-1-11-22-1-11111-1-12i−2i−2i2i0000000000000000−i−iiiii−i−i00000000
χ5022-2-2-222-2-222-2-2-2222-22-2-222-1-2-22-111-2-211-1-122-1-212-11111-1-1-1-11-22-1-11111-1-1−2i2i2i−2i0000000000000000ii−i−i−i−iii00000000
χ5122-2-2-222-2-222-2-2-2222-22-2-22-1211-12-2-211-2-222-1-1-11-2-121111-1-1-12-21-1-1-11111-1-1000000002-2-220000000000000000-1-11111-1-1
χ5222-2-2-222-2-222-2-2-2222-22-2-22-1211-12-2-211-2-222-1-1-11-2-121111-1-1-12-21-1-1-11111-1-100000000-222-2000000000000000011-1-1-1-111
χ534444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-211111111000000000000000000000000000000000000
χ544444444-4-4-4-44444444-4-4-4-4-2-2-2-2-2-2-2-2222222221-2-2-2-211111112222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ554444-4-444-4-444-4-4-4-44444-4-4-2-2-2-2-2-2-2-2-2-22222-2-21222211-1-1-1-11-2-2221111-1-1-1-1000000000000000000000000000000000000
χ564444-4-44-444-44-4-4-4-444-4-444-2-2-2-2-2-2-2-222-2-2-2-2221222211-1-1-1-1122-2-2-1-1-1-11111000000000000000000000000000000000000
χ5744-4-44-444-44-4-444-4-44-4-44-44-2-222-2-222-2-222-2-2221-2-222-1-111-1-112-22-2-1-111-1-111000000000000000000000000000000000000
χ5844-4-44-44-44-44-444-4-44-44-44-4-2-222-2-22222-2-222-2-21-2-222-1-111-1-11-22-2211-1-111-1-1000000000000000000000000000000000000
χ5944-4-4-44444-4-4-4-4-4444-4-444-4-2-222-2-222-2-2-2-22222122-2-2-1-1-1-11112-2-22-1-11111-1-1000000000000000000000000000000000000
χ6044-4-4-444-4-444-4-4-4444-44-4-44-2-222-2-2222222-2-2-2-2122-2-2-1-1-1-1111-222-211-1-1-1-111000000000000000000000000000000000000
χ614-44-4004000040000-4-40000444-4-4-44-400000000400004-40000-4000000000000000000000000000000000000000000000000
χ624-44-4004000040000-4-400004-24-4-42-220023−2323−2300-20000-22000020000000023−2323−23000000000000000000000000000000000000
χ634-44-4004000040000-4-400004-24-4-42-2200−2323−232300-20000-220000200000000−2323−2323000000000000000000000000000000000000
χ644-44-4004000040000-4-40000-24-222-44-423−23000023−23-20000-2200002000023−2323−230000000000000000000000000000000000000000
χ654-44-4004000040000-4-40000-24-222-44-4−23230000−2323-20000-22000020000−2323−23230000000000000000000000000000000000000000
χ664-44-4004000040000-4-40000-2-2-2222-2223−2323−2323−2323−23100001-13-33-3-10000−33−33−33−33000000000000000000000000000000000000
χ674-44-4004000040000-4-40000-2-2-2222-2223−23−2323−232323−23100001-1-33-33-10000−33−333−33−3000000000000000000000000000000000000
χ684-44-4004000040000-4-40000-2-2-2222-22−232323−2323−23−2323100001-1-33-33-100003−33−3−33−33000000000000000000000000000000000000
χ694-44-4004000040000-4-40000-2-2-2222-22−2323−2323−2323−2323100001-13-33-3-100003−33−33−33−3000000000000000000000000000000000000
χ704-4-440040000-40000-44000044-44-4-4-440000000040000-440000-4000000000000000000000000000000000000000000000000
χ714-4-440040000-40000-4400004-2-44-422-20023−23−232300-200002-2000020000000023−23−2323000000000000000000000000000000000000
χ724-4-440040000-40000-4400004-2-44-422-200−232323−2300-200002-20000200000000−232323−23000000000000000000000000000000000000
χ734-4-440040000-40000-440000-242-22-4-4423−230000−2323-200002-2000020000−232323−230000000000000000000000000000000000000000
χ744-4-440040000-40000-440000-242-22-4-44−2323000023−23-200002-200002000023−23−23230000000000000000000000000000000000000000
χ754-4-440040000-40000-440000-2-22-2222-223−2323−23−2323−232310000-11-333-3-100003−3−33−333−3000000000000000000000000000000000000
χ764-4-440040000-40000-440000-2-22-2222-223−23−232323−23−232310000-113-3-33-100003−3−333−3−33000000000000000000000000000000000000
χ774-4-440040000-40000-440000-2-22-2222-2−232323−23−232323−2310000-113-3-33-10000−333−3−333−3000000000000000000000000000000000000
χ784-4-440040000-40000-440000-2-22-2222-2−2323−232323−2323−2310000-11-333-3-10000−333−33−3−33000000000000000000000000000000000000
χ79666666-36666-3-3-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000000022220000-1-1-1-1-1-1-1-10000000000000000
χ80666666-36666-3-3-3-3-3-3-3-3-3-3-300000000000000000000000000000000000000000000-2-2-2-20000111111110000000000000000
χ81666666-3-6-6-6-6-3-3-3-3-3-3-333330000000000000000000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i30000000000000000
χ82666666-3-6-6-6-6-3-3-3-3-3-3-333330000000000000000000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i30000000000000000
χ836666-6-6-36-6-66-33333-3-3-3-3330000000000000000000000000000000000000000000022-2-20000-1-1-1-111110000000000000000
χ846666-6-6-36-6-66-33333-3-3-3-33300000000000000000000000000000000000000000000-2-22200001111-1-1-1-10000000000000000
χ856666-6-6-3-666-6-33333-3-333-3-30000000000000000000000000000000000000000000000000000−i3i3−i3i3i3−i3i3−i30000000000000000
χ866666-6-6-3-666-6-33333-3-333-3-30000000000000000000000000000000000000000000000000000i3−i3i3−i3−i3i3−i3i30000000000000000
χ8766-6-66-6-36-66-63-3-333-333-33-300000000000000000000000000000000000000000000000000003−3−333−3−330000000000000000
χ8866-6-66-6-36-66-63-3-333-333-33-30000000000000000000000000000000000000000000000000000−333−3−333−30000000000000000
χ8966-6-66-6-3-66-663-3-333-33-33-33000000000000000000000000000000000000000000002i−2i2i−2i0000−i−iii−i−iii0000000000000000
χ9066-6-66-6-3-66-663-3-333-33-33-3300000000000000000000000000000000000000000000−2i2i−2i2i0000ii−i−iii−i−i0000000000000000
χ9166-6-6-66-366-6-6333-3-3-333-3-3300000000000000000000000000000000000000000000000000003−3−33−333−30000000000000000
χ9266-6-6-66-366-6-6333-3-3-333-3-330000000000000000000000000000000000000000000000000000−333−33−3−330000000000000000
χ9366-6-6-66-3-6-666333-3-3-33-333-3000000000000000000000000000000000000000000002i−2i−2i2i0000−i−iiiii−i−i0000000000000000
χ9466-6-6-66-3-6-666333-3-3-33-333-300000000000000000000000000000000000000000000−2i2i2i−2i0000ii−i−i−i−iii0000000000000000
χ9512-1212-1200-60000-6−6i36i3−6i36i36600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9612-1212-1200-60000-66i3−6i36i3−6i36600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12-121200-600006−6i36i36i3−6i36-600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-121200-6000066i3−6i3−6i36i36-600000000000000000000000000000000000000000000000000000000000000000000000000000000

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