Finite Group Databasebeta

← Group #13147917

Character table — Group #13147917

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order1222344446664121212121212336666661212121212121212366612121212121212121212121212121212121212122222444422444444666666121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11-1-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-111-1-1111-1-1-1-1-11-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-111-1-1-1-111111-1-111-1-1-1-111-1-111-1-1
χ61111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1111-11-111-1-11111-1-1-1-1-1-111-1-111
χ71111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-111
χ81111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1111-1-1-1-111-1-11111-1-11111-1-1
χ911111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-11-1-11-11111-1-1-1-111-1-1-1-1111-11-1
χ1011111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111111-1-1-11-1-1111-1-111-1-111-1-111-1-1-11-11
χ1111111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11-11111-1-111-1-111-1-111-1-111-11-11
χ1211111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-11-1-1-1-1-1-11111-1-11111-1-11-11-1
χ1311111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1111111-1-1-1-111-1-1-1-11-1-11
χ1411111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-11-111111-1-1-1-1-1-1-1-1111111-111-1
χ1511111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-11-111-1-1-11-1-111111111-1-1-1-1-1-1-111-1
χ1611111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-11-11-1-1-1-1-1-1-11111-1-111111-1-11
χ1722222222222222222222-1-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1002200222000002000-1-1-1-1000000-1-1-1-10000
χ1822222222222222222222-1-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-2-200000-2000111100000011110000
χ192222222222222222222-1222-1-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12200220000200200-1-10000-1-1-1-1-1-100000000
χ202222222222222222222-1222-1-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20000-200-20011000011111100000000
χ212222222-2-2222-222-2-2-2-22-1-1-1222-122221111-1-1-1-1-1-111-2-2-2-2-1-1-1-11111111100220022-200000-2000-1-111000000-1-1110000
χ222222222-2-2222-222-2-2-2-22-1-1-1222-122221111-1-1-1-1-1-111-2-2-2-2-1-1-1-11111111100-2-200-2-2200000200011-1-100000011-1-10000
χ232222222-2-2222-222-2-2-2-2-1222-1-1-12-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-1111111112200-2-20000200-200-1-10000-1-1111100000000
χ242222222-2-2222-222-2-2-2-2-1222-1-1-12-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-111111111-2-200220000-20020011000011-1-1-1-100000000
χ2522222-2-222222-2-2-222-2-22-1-1-1222-1-2-2-2-2-1-1-1-1-1-1-1-1111122-2-21111-1-1-1-11111002200-2-2-2000002000-1-11100000011-1-10000
χ2622222-2-222222-2-2-222-2-22-1-1-1222-1-2-2-2-2-1-1-1-1-1-1-1-1111122-2-21111-1-1-1-1111100-2-20022200000-200011-1-1000000-1-1110000
χ2722222-2-222222-2-2-222-2-2-1222-1-1-1211112222-1-1-1-1-2-2-2-2-1-1111111-1-1-1-111112200220000-200-200-1-1000011-1-11100000000
χ2822222-2-222222-2-2-222-2-2-1222-1-1-1211112222-1-1-1-1-2-2-2-2-1-1111111-1-1-1-11111-2-200-2-20000200200110000-1-111-1-100000000
χ2922222-2-2-2-22222-2-2-2-2222-1-1-1222-1-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-1002200-2-2200000-2000-1-1-1-100000011110000
χ3022222-2-2-2-22222-2-2-2-2222-1-1-1222-1-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-100-2-20022-20000020001111000000-1-1-1-10000
χ3122222-2-2-2-22222-2-2-2-222-1222-1-1-121111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-12200-2-20000-200200-1-100001111-1-100000000
χ3222222-2-2-2-22222-2-2-2-222-1222-1-1-121111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-1-2-200220000200-200110000-1-1-1-11100000000
χ3322-2-22002i−2i2-2-20002i−2i00222-22-2-2-200002i2i−2i−2i22-2-200002i−2i0000002i2i−2i−2i00002-2002i−2i00000000002-20000002i−2i0000000000
χ3422-2-22002i−2i2-2-20002i−2i00222-22-2-2-200002i2i−2i−2i22-2-200002i−2i0000002i2i−2i−2i0000-2200−2i2i0000000000-22000000−2i2i0000000000
χ3522-2-22002i−2i2-2-20002i−2i00-122-2-111-2−i3−i3i3i32i2i−2i−2i-1-1110000−ii3−3−i3−i3i3i3−i−iii33−3−32-2002i−2i0000000000-110000−i3i3−ii3−300000000
χ3622-2-22002i−2i2-2-20002i−2i00-122-2-111-2−i3−i3i3i32i2i−2i−2i-1-1110000−ii3−3−i3−i3i3i3−i−iii33−3−3-2200−2i2i00000000001-10000i3−i3i−i−3300000000
χ3722-2-22002i−2i2-2-20002i−2i00-122-2-111-2i3i3−i3−i32i2i−2i−2i-1-1110000−ii−33i3i3−i3−i3−i−iii−3−3332-2002i−2i0000000000-110000i3−i3−ii−3300000000
χ3822-2-22002i−2i2-2-20002i−2i00-122-2-111-2i3i3−i3−i32i2i−2i−2i-1-1110000−ii−33i3i3−i3−i3−i−iii−3−333-2200−2i2i00000000001-10000−i3i3i−i3−300000000
χ3922-2-2200−2i2i2-2-2000−2i2i00222-22-2-2-20000−2i−2i2i2i22-2-20000−2i2i000000−2i−2i2i2i00002-200−2i2i00000000002-2000000−2i2i0000000000
χ4022-2-2200−2i2i2-2-2000−2i2i00222-22-2-2-20000−2i−2i2i2i22-2-20000−2i2i000000−2i−2i2i2i0000-22002i−2i0000000000-220000002i−2i0000000000
χ4122-2-2200−2i2i2-2-2000−2i2i00-122-2-111-2−i3−i3i3i3−2i−2i2i2i-1-1110000i−i−33−i3−i3i3i3ii−i−i−3−3332-200−2i2i0000000000-110000−i3i3i−i−3300000000
χ4222-2-2200−2i2i2-2-2000−2i2i00-122-2-111-2−i3−i3i3i3−2i−2i2i2i-1-1110000i−i−33−i3−i3i3i3ii−i−i−3−333-22002i−2i00000000001-10000i3−i3−ii3−300000000
χ4322-2-2200−2i2i2-2-2000−2i2i00-122-2-111-2i3i3−i3−i3−2i−2i2i2i-1-1110000i−i3−3i3i3−i3−i3ii−i−i33−3−32-200−2i2i0000000000-110000i3−i3i−i3−300000000
χ4422-2-2200−2i2i2-2-2000−2i2i00-122-2-111-2i3i3−i3−i3−2i−2i2i2i-1-1110000i−i3−3i3i3−i3−i3ii−i−i33−3−3-22002i−2i00000000001-10000−i3i3−ii−3300000000
χ452-22-222i−2i00-22-202i−2i000022-22-22-2-22i−2i2i−2i00002-22-22i−2i0000002i−2i2i−2i00000000002-2002i−2i00000000002-2000000002i−2i000000
χ462-22-222i−2i00-22-202i−2i000022-22-22-2-22i−2i2i−2i00002-22-22i−2i0000002i−2i2i−2i0000000000-2200−2i2i0000000000-2200000000−2i2i000000
χ472-22-222i−2i00-22-202i−2i00002-11-1-22-212i−2i2i−2i3−33−3-11-11−ii−i3i30000−ii−ii3−33−3−i3i3−i3i3002-2002i−2i0000000000-11−i3i3000000−ii3−30000
χ482-22-222i−2i00-22-202i−2i00002-11-1-22-212i−2i2i−2i3−33−3-11-11−ii−i3i30000−ii−ii3−33−3−i3i3−i3i300-2200−2i2i00000000001-1i3−i3000000i−i−330000
χ492-22-222i−2i00-22-202i−2i00002-11-1-22-212i−2i2i−2i−33−33-11-11−iii3−i30000−ii−ii−33−33i3−i3i3−i3002-2002i−2i0000000000-11i3−i3000000−ii−330000
χ502-22-222i−2i00-22-202i−2i00002-11-1-22-212i−2i2i−2i−33−33-11-11−iii3−i30000−ii−ii−33−33i3−i3i3−i300-2200−2i2i00000000001-1−i3i3000000i−i3−30000
χ512-22-22−2i2i00-22-20−2i2i000022-22-22-2-2−2i2i−2i2i00002-22-2−2i2i000000−2i2i−2i2i00000000002-200−2i2i00000000002-200000000−2i2i000000
χ522-22-22−2i2i00-22-20−2i2i000022-22-22-2-2−2i2i−2i2i00002-22-2−2i2i000000−2i2i−2i2i0000000000-22002i−2i0000000000-22000000002i−2i000000
χ532-22-22−2i2i00-22-20−2i2i00002-11-1-22-21−2i2i−2i2i3−33−3-11-11i−ii3−i30000i−ii−i3−33−3i3−i3i3−i3002-200−2i2i0000000000-11i3−i3000000i−i3−30000
χ542-22-22−2i2i00-22-20−2i2i00002-11-1-22-21−2i2i−2i2i3−33−3-11-11i−ii3−i30000i−ii−i3−33−3i3−i3i3−i300-22002i−2i00000000001-1−i3i3000000−ii−330000
χ552-22-22−2i2i00-22-20−2i2i00002-11-1-22-21−2i2i−2i2i−33−33-11-11i−i−i3i30000i−ii−i−33−33−i3i3−i3i3002-200−2i2i0000000000-11−i3i3000000i−i−330000
χ562-22-22−2i2i00-22-20−2i2i00002-11-1-22-21−2i2i−2i2i−33−33-11-11i−i−i3i30000i−ii−i−33−33−i3i3−i3i300-22002i−2i00000000001-1i3−i3000000−ii3−30000
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
χ5944444-4-444444-4-4-444-4-4-2-2-2-2-2-2-2-22222-2-2-2-211112222-2-222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000
χ6044444-4-4-4-44444-4-4-4-444-2-2-2-2-2-2-2-222222222111122-2-222-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000000000
χ6144-4-44004i−4i4-4-40004i−4i004-2-224-4-420000−2i−2i2i2i-2-22200004i−4i000000−2i−2i2i2i0000000000000000000000000000000000000000
χ6244-4-44004i−4i4-4-40004i−4i00-2-2-22-2222−2i3−2i32i32i3−2i−2i2i2i11-1-10000−2i2i23−23i3i3−i3−i3ii−i−i−3−333000000000000000000000000000000000000
χ6344-4-44004i−4i4-4-40004i−4i00-2-2-22-22222i32i3−2i3−2i3−2i−2i2i2i11-1-10000−2i2i−2323−i3−i3i3i3ii−i−i33−3−3000000000000000000000000000000000000
χ6444-4-4400−4i4i4-4-4000−4i4i004-2-224-4-4200002i2i−2i−2i-2-2220000−4i4i0000002i2i−2i−2i0000000000000000000000000000000000000000
χ6544-4-4400−4i4i4-4-4000−4i4i00-2-2-22-2222−2i3−2i32i32i32i2i−2i−2i11-1-100002i−2i−2323i3i3−i3−i3−i−iii33−3−3000000000000000000000000000000000000
χ6644-4-4400−4i4i4-4-4000−4i4i00-2-2-22-22222i32i3−2i3−2i32i2i−2i−2i11-1-100002i−2i23−23−i3−i3i3i3−i−iii−3−333000000000000000000000000000000000000
χ674-44-444i−4i00-44-404i−4i0000-24-442-22-4−2i2i−2i2i0000-22-224i−4i000000−2i2i−2i2i00000000000000000000000000000000000000000000
χ684-44-444i−4i00-44-404i−4i0000-2-22-22-222−2i2i−2i2i23−2323−231-11-1−2i2i−2i32i30000i−ii−i−33−33i3−i3i3−i3000000000000000000000000000000000000
χ694-44-444i−4i00-44-404i−4i0000-2-22-22-222−2i2i−2i2i−2323−23231-11-1−2i2i2i3−2i30000i−ii−i3−33−3−i3i3−i3i3000000000000000000000000000000000000
χ704-44-44−4i4i00-44-40−4i4i0000-24-442-22-42i−2i2i−2i0000-22-22−4i4i0000002i−2i2i−2i00000000000000000000000000000000000000000000
χ714-44-44−4i4i00-44-40−4i4i0000-2-22-22-2222i−2i2i−2i23−2323−231-11-12i−2i2i3−2i30000−ii−ii−33−33−i3i3−i3i3000000000000000000000000000000000000
χ724-44-44−4i4i00-44-40−4i4i0000-2-22-22-2222i−2i2i−2i−2323−23231-11-12i−2i−2i32i30000−ii−ii3−33−3i3−i3i3−i3000000000000000000000000000000000000
χ734-4-4440000-4-44000000044-4-4-4-444000000004-4-4400000000000000000000000000000000000000000000000000000000
χ744-4-4440000-4-4400000004-222-4-44-20000−2i32i32i3−2i3-222-2000000000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ754-4-4440000-4-4400000004-222-4-44-200002i3−2i3−2i32i3-222-20000000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ764-4-4440000-4-440000000-24-4-422-2423−23−23230000-222-20000000023−23−232300000000000000000000000000000000000000000000
χ774-4-4440000-4-440000000-24-4-422-24−232323−230000-222-200000000−232323−2300000000000000000000000000000000000000000000
χ784-4-4440000-4-440000000-2-22222-2-223−23−2323−2i32i32i3−2i31-1-1100000000−333−3i3−i3−i3i33i−3i−3i3i000000000000000000000000000000000000
χ794-4-4440000-4-440000000-2-22222-2-223−23−23232i3−2i3−2i32i31-1-1100000000−333−3−i3i3i3−i3−3i3i3i−3i000000000000000000000000000000000000
χ804-4-4440000-4-440000000-2-22222-2-2−232323−23−2i32i32i3−2i31-1-11000000003−3−33i3−i3−i3i3−3i3i3i−3i000000000000000000000000000000000000
χ814-4-4440000-4-440000000-2-22222-2-2−232323−232i3−2i3−2i32i31-1-11000000003−3−33−i3i3i3−i33i−3i−3i3i000000000000000000000000000000000000
χ826666-36666-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000020220020000000000000000-1-1-1-1
χ836666-36666-3-3-36-3-3-3-3-3-30000000000000000000000000000000000000000000000000-20-2-200-200000000000000001111
χ846666-366-6-6-3-3-3-6-3-33333000000000000000000000000000000000000000000000000020-2-20020000000000000000-1-111
χ856666-366-6-6-3-3-3-6-3-333330000000000000000000000000000000000000000000000000-202200-2000000000000000011-1-1
χ866666-3-6-666-3-3-3-633-3-3330000000000000000000000000000000000000000000000000202-200-20000000000000000-11-11
χ876666-3-6-666-3-3-3-633-3-3330000000000000000000000000000000000000000000000000-20-2200200000000000000001-11-1
χ886666-3-6-6-6-6-3-3-363333-3-3000000000000000000000000000000000000000000000000020-2200-20000000000000000-111-1
χ896666-3-6-6-6-6-3-3-363333-3-30000000000000000000000000000000000000000000000000-202-200200000000000000001-1-11
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
χ9412-12-1212-6000066-60000063−630000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-6000066-600000−63630000000000000000000000000000000000000000000000000000000000000000000000000000

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