Finite Group Databasebeta

← Group #13147916

Character table — Group #13147916

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order12223444466641212121212123366666612121212121212123666121212121212121212121212121212121212121222224444224444446666121212121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11-1-1-11-11-1111111-1-1-1-111-1-1-1-11-11-1
χ61111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-11-1-1-11-1111-1-111-1-1-1-1-1-11111-11-11
χ71111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-11-1-111-1-1111111-1-1-1-1-11-11
χ81111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-111-1-1-1-1-1-1-11111-1-111111-11-1
χ911111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-11-1-1-1-111111-1-111-1-1-1-111-1-11-1-11
χ1011111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111-1111-111-1-1-1-111-1-111-1-111-111-1
χ1111111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-11-11-1-11-1-1-11111-1-111-1-111-1-1-111-1
χ1211111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-1-1111-11-1-1-1-111-1-11111-1-1111-1-11
χ1311111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-11-11-1-11111-1-1-1-111-1-1-1-11111-1-1
χ1411111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-111-11111-1-1-1-1-1-1111111-1-1-1-111
χ1511111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1111-1-1111111-1-1-1-1-1-111-1-111
χ1611111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111-11-1-1-1-1-1-1-11111-1-11111-1-111-1-1
χ1722222222222222222222-1222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12200220000220000-1-100-1-1-1-1-1-10000000000
χ1822222222222222222222-1222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20000-2-2000011001111110000000000
χ192222222222222222222-12-1-1-1222-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1002200220000220000-1-1000000-1-1-1-1-1-10000
χ202222222222222222222-12-1-1-1222-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-20000-2-20000110000001111110000
χ212222222-2-2222-222-2-2-2-22-1222-1-1-122221111-1-1-1-1-1-1-2-2-2-211-1-1-1-1111111112200220000-2-20000-1-100-1-111110000000000
χ222222222-2-2222-222-2-2-2-22-1222-1-1-122221111-1-1-1-1-1-1-2-2-2-211-1-1-1-111111111-2-200-2-20000220000110011-1-1-1-10000000000
χ232222222-2-2222-222-2-2-2-2-12-1-1-1222-1-1-1-1-2-2-2-2-1-1-1-1221111-2-2-1-1-1-111111111002200-2-200002-20000-1-1000000-1-111110000
χ242222222-2-2222-222-2-2-2-2-12-1-1-1222-1-1-1-1-2-2-2-2-1-1-1-1221111-2-2-1-1-1-11111111100-2-200220000-2200001100000011-1-1-1-10000
χ2522222-2-222222-2-2-222-2-22-1222-1-1-1-2-2-2-2-1-1-1-1-1-1-1-11122-2-2111111-1-1-1-111112200-2-200002-20000-1-10011-1-1110000000000
χ2622222-2-222222-2-2-222-2-22-1222-1-1-1-2-2-2-2-1-1-1-1-1-1-1-11122-2-2111111-1-1-1-11111-2-200220000-2200001100-1-111-1-10000000000
χ2722222-2-222222-2-2-222-2-2-12-1-1-122211112222-1-1-1-1-2-2-1-111-2-21111-1-1-1-11111002200220000-2-20000-1-100000011-1-1110000
χ2822222-2-222222-2-2-222-2-2-12-1-1-122211112222-1-1-1-1-2-2-1-111-2-21111-1-1-1-1111100-2-200-2-2000022000011000000-1-111-1-10000
χ2922222-2-2-2-22222-2-2-2-2222-1222-1-1-1-2-2-2-21111-1-1-1-111-2-222-1-111111111-1-1-1-12200-2-20000-220000-1-1001111-1-10000000000
χ3022222-2-2-2-22222-2-2-2-2222-1222-1-1-1-2-2-2-21111-1-1-1-111-2-222-1-111111111-1-1-1-1-2-2002200002-200001100-1-1-1-1110000000000
χ3122222-2-2-2-22222-2-2-2-222-12-1-1-12221111-2-2-2-2-1-1-1-1-2-211-1-12211111111-1-1-1-1002200-2-20000-220000-1-10000001111-1-10000
χ3222222-2-2-2-22222-2-2-2-222-12-1-1-12221111-2-2-2-2-1-1-1-1-2-211-1-12211111111-1-1-1-100-2-2002200002-2000011000000-1-1-1-1110000
χ3322-2-22002i−2i2-2-20002i−2i00222-2-22-2-200002i2i−2i−2i22-2-2002i−2i000000002i2i−2i−2i0000002-2002i−2i00000000002-2000000002i−2i000000
χ3422-2-22002i−2i2-2-20002i−2i00222-2-22-2-200002i2i−2i−2i22-2-2002i−2i000000002i2i−2i−2i000000-2200−2i2i0000000000-2200000000−2i2i000000
χ3522-2-22002i−2i2-2-20002i−2i00-12-1112-2-2−i3−i3i3i32i2i−2i−2i-1-11100−ii3−300−i3−i3i3i3−i−iii33−3−3002-2002i−2i0000000000-11000000−i3i3−ii3−30000
χ3622-2-22002i−2i2-2-20002i−2i00-12-1112-2-2−i3−i3i3i32i2i−2i−2i-1-11100−ii3−300−i3−i3i3i3−i−iii33−3−300-2200−2i2i00000000001-1000000i3−i3i−i−330000
χ3722-2-22002i−2i2-2-20002i−2i00-12-1112-2-2i3i3−i3−i32i2i−2i−2i-1-11100−ii−3300i3i3−i3−i3−i−iii−3−333002-2002i−2i0000000000-11000000i3−i3−ii−330000
χ3822-2-22002i−2i2-2-20002i−2i00-12-1112-2-2i3i3−i3−i32i2i−2i−2i-1-11100−ii−3300i3i3−i3−i3−i−iii−3−33300-2200−2i2i00000000001-1000000−i3i3i−i3−30000
χ3922-2-2200−2i2i2-2-2000−2i2i00222-2-22-2-20000−2i−2i2i2i22-2-200−2i2i00000000−2i−2i2i2i0000002-200−2i2i00000000002-200000000−2i2i000000
χ4022-2-2200−2i2i2-2-2000−2i2i00222-2-22-2-20000−2i−2i2i2i22-2-200−2i2i00000000−2i−2i2i2i000000-22002i−2i0000000000-22000000002i−2i000000
χ4122-2-2200−2i2i2-2-2000−2i2i00-12-1112-2-2−i3−i3i3i3−2i−2i2i2i-1-11100i−i−3300−i3−i3i3i3ii−i−i−3−333002-200−2i2i0000000000-11000000−i3i3i−i−330000
χ4222-2-2200−2i2i2-2-2000−2i2i00-12-1112-2-2−i3−i3i3i3−2i−2i2i2i-1-11100i−i−3300−i3−i3i3i3ii−i−i−3−33300-22002i−2i00000000001-1000000i3−i3−ii3−30000
χ4322-2-2200−2i2i2-2-2000−2i2i00-12-1112-2-2i3i3−i3−i3−2i−2i2i2i-1-11100i−i3−300i3i3−i3−i3ii−i−i33−3−3002-200−2i2i0000000000-11000000i3−i3i−i3−30000
χ4422-2-2200−2i2i2-2-2000−2i2i00-12-1112-2-2i3i3−i3−i3−2i−2i2i2i-1-11100i−i3−300i3i3−i3−i3ii−i−i33−3−300-22002i−2i00000000001-1000000−i3i3−ii−330000
χ452-22-222i−2i00-22-202i−2i000022-22-2-22-22i−2i2i−2i00002-22-22i−2i0000002i−2i2i−2i000000002-2002i−2i00000000002-2002i−2i00000000000000
χ462-22-222i−2i00-22-202i−2i000022-22-2-22-22i−2i2i−2i00002-22-22i−2i0000002i−2i2i−2i00000000-2200−2i2i0000000000-2200−2i2i00000000000000
χ472-22-222i−2i00-22-202i−2i00002-1-22-21-112i−2i2i−2i−i3i3−i3i3-11-11−ii00003−3−ii−ii−i3i3−i3i33−33−32-2002i−2i0000000000-1100−ii−i3i33−30000000000
χ482-22-222i−2i00-22-202i−2i00002-1-22-21-112i−2i2i−2i−i3i3−i3i3-11-11−ii00003−3−ii−ii−i3i3−i3i33−33−3-2200−2i2i00000000001-100i−ii3−i3−330000000000
χ492-22-222i−2i00-22-202i−2i00002-1-22-21-112i−2i2i−2ii3−i3i3−i3-11-11−ii0000−33−ii−iii3−i3i3−i3−33−332-2002i−2i0000000000-1100−iii3−i3−330000000000
χ502-22-222i−2i00-22-202i−2i00002-1-22-21-112i−2i2i−2ii3−i3i3−i3-11-11−ii0000−33−ii−iii3−i3i3−i3−33−33-2200−2i2i00000000001-100i−i−i3i33−30000000000
χ512-22-22−2i2i00-22-20−2i2i000022-22-2-22-2−2i2i−2i2i00002-22-2−2i2i000000−2i2i−2i2i000000002-200−2i2i00000000002-200−2i2i00000000000000
χ522-22-22−2i2i00-22-20−2i2i000022-22-2-22-2−2i2i−2i2i00002-22-2−2i2i000000−2i2i−2i2i00000000-22002i−2i0000000000-22002i−2i00000000000000
χ532-22-22−2i2i00-22-20−2i2i00002-1-22-21-11−2i2i−2i2i−i3i3−i3i3-11-11i−i0000−33i−ii−i−i3i3−i3i3−33−332-200−2i2i0000000000-1100i−i−i3i3−330000000000
χ542-22-22−2i2i00-22-20−2i2i00002-1-22-21-11−2i2i−2i2i−i3i3−i3i3-11-11i−i0000−33i−ii−i−i3i3−i3i3−33−33-22002i−2i00000000001-100−iii3−i33−30000000000
χ552-22-22−2i2i00-22-20−2i2i00002-1-22-21-11−2i2i−2i2ii3−i3i3−i3-11-11i−i00003−3i−ii−ii3−i3i3−i33−33−32-200−2i2i0000000000-1100i−ii3−i33−30000000000
χ562-22-22−2i2i00-22-20−2i2i00002-1-22-21-11−2i2i−2i2ii3−i3i3−i3-11-11i−i00003−3i−ii−ii3−i3i3−i33−33−3-22002i−2i00000000001-100−ii−i3i3−330000000000
χ574444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000
χ584444444-4-4444-444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-222221111-2-22222221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5944444-4-444444-4-4-444-4-4-2-2-2-2-2-2-2-22222-2-2-2-2111122-2-22222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000
χ6044444-4-4-4-44444-4-4-4-444-2-2-2-2-2-2-2-22222222211112222-2-2-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000000000
χ6144-4-44004i−4i4-4-40004i−4i004-24-4-4-2220000−2i−2i2i2i-2-222004i−4i00000000−2i−2i2i2i0000000000000000000000000000000000000000
χ6244-4-44004i−4i4-4-40004i−4i00-2-2-222-222−2i3−2i32i32i3−2i−2i2i2i11-1-100−2i2i23−2300i3i3−i3−i3ii−i−i−3−333000000000000000000000000000000000000
χ6344-4-44004i−4i4-4-40004i−4i00-2-2-222-2222i32i3−2i3−2i3−2i−2i2i2i11-1-100−2i2i−232300−i3−i3i3i3ii−i−i33−3−3000000000000000000000000000000000000
χ6444-4-4400−4i4i4-4-4000−4i4i004-24-4-4-22200002i2i−2i−2i-2-22200−4i4i000000002i2i−2i−2i0000000000000000000000000000000000000000
χ6544-4-4400−4i4i4-4-4000−4i4i00-2-2-222-222−2i3−2i32i32i32i2i−2i−2i11-1-1002i−2i−232300i3i3−i3−i3−i−iii33−3−3000000000000000000000000000000000000
χ6644-4-4400−4i4i4-4-4000−4i4i00-2-2-222-2222i32i3−2i3−2i32i2i−2i−2i11-1-1002i−2i23−2300−i3−i3i3i3−i−iii−3−333000000000000000000000000000000000000
χ674-44-444i−4i00-44-404i−4i0000-242-22-44-4−2i2i−2i2i0000-22-224i−4i000000−2i2i−2i2i00000000000000000000000000000000000000000000
χ684-44-444i−4i00-44-404i−4i0000-2-22-222-22−2i2i−2i2i−2i32i3−2i32i31-11-1−2i2i000023−23i−ii−ii3−i3i3−i3−33−33000000000000000000000000000000000000
χ694-44-444i−4i00-44-404i−4i0000-2-22-222-22−2i2i−2i2i2i3−2i32i3−2i31-11-1−2i2i0000−2323i−ii−i−i3i3−i3i33−33−3000000000000000000000000000000000000
χ704-44-44−4i4i00-44-40−4i4i0000-242-22-44-42i−2i2i−2i0000-22-22−4i4i0000002i−2i2i−2i00000000000000000000000000000000000000000000
χ714-44-44−4i4i00-44-40−4i4i0000-2-22-222-222i−2i2i−2i−2i32i3−2i32i31-11-12i−2i0000−2323−ii−iii3−i3i3−i33−33−3000000000000000000000000000000000000
χ724-44-44−4i4i00-44-40−4i4i0000-2-22-222-222i−2i2i−2i2i3−2i32i3−2i31-11-12i−2i000023−23−ii−ii−i3i3−i3i3−33−33000000000000000000000000000000000000
χ734-4-4440000-4-44000000044-4-44-4-44000000004-4-4400000000000000000000000000000000000000000000000000000000
χ744-4-4440000-4-4400000004-2-4-4422-2000023−23−2323-222-200000000000023−23−23230000000000000000000000000000000000000000
χ754-4-4440000-4-4400000004-2-4-4422-20000−232323−23-222-2000000000000−232323−230000000000000000000000000000000000000000
χ764-4-4440000-4-440000000-2422-2-4-4423−23−23230000-222-20000000023−23−232300000000000000000000000000000000000000000000
χ774-4-4440000-4-440000000-2422-2-4-44−232323−230000-222-200000000−232323−2300000000000000000000000000000000000000000000
χ784-4-4440000-4-440000000-2-222-222-223−23−232323−23−23231-1-1100000000−333−3−333−33-3-33000000000000000000000000000000000000
χ794-4-4440000-4-440000000-2-222-222-223−23−2323−232323−231-1-1100000000−333−33−3−33-333-3000000000000000000000000000000000000
χ804-4-4440000-4-440000000-2-222-222-2−232323−2323−23−23231-1-11000000003−3−33−333−3-333-3000000000000000000000000000000000000
χ814-4-4440000-4-440000000-2-222-222-2−232323−23−232323−231-1-11000000003−3−333−3−333-3-33000000000000000000000000000000000000
χ826666-36666-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000220000220000000000000000-1-1-1-1
χ836666-36666-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000-2-20000-2-200000000000000001111
χ846666-366-6-6-3-3-3-6-3-333330000000000000000000000000000000000000000000000002-200002-20000000000000000-11-11
χ856666-366-6-6-3-3-3-6-3-33333000000000000000000000000000000000000000000000000-220000-2200000000000000001-11-1
χ866666-3-6-666-3-3-3-633-3-3330000000000000000000000000000000000000000000000002-20000-220000000000000000-111-1
χ876666-3-6-666-3-3-3-633-3-333000000000000000000000000000000000000000000000000-2200002-200000000000000001-1-11
χ886666-3-6-6-6-6-3-3-363333-3-3000000000000000000000000000000000000000000000000220000-2-20000000000000000-1-111
χ896666-3-6-6-6-6-3-3-363333-3-3000000000000000000000000000000000000000000000000-2-2000022000000000000000011-1-1
χ901212-12-12-60012i−12i-666000−6i6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ911212-12-12-600−12i12i-6660006i−6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9212-1212-12-612i−12i006-660−6i6i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-12-6−12i12i006-6606i−6i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-1212-6000066-600000−6i36i30000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-6000066-6000006i3−6i30000000000000000000000000000000000000000000000000000000000000000000000000000

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