Finite Group Databasebeta

← Group #13150847

Character table — Group #13150847

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order122234444666266121212123366666612121212121212123666666666661212121212121212121212122244444422444444661212121212121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ51111111-1-1111-1-1-111-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-1111111-1-1-1-1111111-1-11-1-1-11-11-11111-1-1-1-11111-1-1-1-11-11-1
χ61111111-1-1111-1-1-111-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-1111111-1-1-1-11111-1-111-11-1-1-11-111111-1-1-1-1-1-1-1-11111-11-11
χ71111111-1-1111-1-1-111-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-111-1-1-11111-1-11-1-1-1-111111111-1-1-1-1-11-11
χ81111111-1-1111-1-1-111-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1111-111-111-1-1-1-1-11111-1-1-1-111111-11-1
χ911111-1-111111-1-1-1-1-11111111111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1111111-1-11111-1-11-1-1-11111-1-1-1-11111-1-111-1-1-1-111
χ1011111-1-111111-1-1-1-1-11111111111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1111-111-1-111-1-1-1-111-1-111-1-11111-1-1
χ1111111-1-111111-1-1-1-1-11111111111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-11111-1-111111111-11-1-1-1-1-1-11111-1-111-1-111-1-111-1-1
χ1211111-1-111111-1-1-1-1-11111111111-1-1-1-111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-111111-1-11111-1-1-1-111-1-111-1-111
χ1311111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11-11-111-111-1-111-1-111-1-1-1-111-111-1
χ1411111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-111-1-1111-1-111-1-1-1-11111-1-11-1-11
χ1511111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-11-1-11-11-1-111-1-11111-1-1-1-1111-1-11
χ1611111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111-11-11-1-1-111-1-111-1-11111-1-1-111-1
χ1722222222222222222222-12-1-1-1222222-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222000000220000-1-1-1-1-1-1-1-1000000000000
χ1822222222222222222222-12-1-1-1222222-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000-2-2000011111111000000000000
χ192222222222222222222-12-1222-1-1-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000022220000220000000000-1-1-1-1-1-1-1-10000
χ202222222222222222222-12-1222-1-1-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-20000-2-20000000000111111110000
χ212222222-2-2222-2-2-222-2-22-12-1-1-12222221111-1-2-211-1-11111-1-2-2-1-1-1-1-1-111112222000000-2-20000-1-1-1-11111000000000000
χ222222222-2-2222-2-2-222-2-22-12-1-1-12222221111-1-2-211-1-11111-1-2-2-1-1-1-1-1-11111-2-2-2-20000002200001111-1-1-1-1000000000000
χ232222222-2-2222-2-2-222-2-2-12-1222-1-1-1-1-1-1-2-2-2-2-111-2-2-1-11111-11122-1-1-1-11111000022-2-200002-20000000000-1-1-1-111110000
χ242222222-2-2222-2-2-222-2-2-12-1222-1-1-1-1-1-1-2-2-2-2-111-2-2-1-11111-11122-1-1-1-111110000-2-2220000-2200000000001111-1-1-1-10000
χ2522222-2-222222-2-2-2-2-2222-12-1-1-122-2-2-2-2-1-1-1-1-1-2-211-1-11111-122111111-1-1-1-122-2-20000002-20000-1-11111-1-1000000000000
χ2622222-2-222222-2-2-2-2-2222-12-1-1-122-2-2-2-2-1-1-1-1-1-2-211-1-11111-122111111-1-1-1-1-2-222000000-22000011-1-1-1-111000000000000
χ2722222-2-222222-2-2-2-2-222-12-1222-1-111112222-111-2-2-1-11111-1-1-1-2-21111-1-1-1-1000022220000-2-20000000000-1-111-1-1110000
χ2822222-2-222222-2-2-2-2-222-12-1222-1-111112222-111-2-2-1-11111-1-1-1-2-21111-1-1-1-10000-2-2-2-2000022000000000011-1-111-1-10000
χ2922222-2-2-2-2222222-2-2-2-22-12-1-1-122-2-2-2-21111-122-1-1-1-1-1-1-1-1-1-2-2111111111122-2-2000000-220000-1-111-1-111000000000000
χ3022222-2-2-2-2222222-2-2-2-22-12-1-1-122-2-2-2-21111-122-1-1-1-1-1-1-1-1-1-2-21111111111-2-2220000002-2000011-1-111-1-1000000000000
χ3122222-2-2-2-2222222-2-2-2-2-12-1222-1-11111-2-2-2-2-1-1-122-1-1-1-1-1-1-111-2-211111111000022-2-20000-220000000000-1-11111-1-10000
χ3222222-2-2-2-2222222-2-2-2-2-12-1222-1-11111-2-2-2-2-1-1-122-1-1-1-1-1-1-111-2-2111111110000-2-22200002-2000000000011-1-1-1-1110000
χ3322-2-22002-2-22-2000002-2222-2-22-2-2000022-2-220000-2-2000022-200000022-2-200002i−2i2i−2i00000000000000002i−2i002i−2i000000
χ3422-2-22002-2-22-2000002-2222-2-22-2-2000022-2-220000-2-2000022-200000022-2-20000−2i2i−2i2i0000000000000000−2i2i00−2i2i000000
χ3522-2-22002-2-22-2000002-2-12-1-2-2211−i3−i3i3i322-2-2-1−i3i30011−i3−i3i3i3-1-1100−i3−i3i3i3-1-11100002i−2i2i−2i0000000000000000−ii3−3−ii3−30000
χ3622-2-22002-2-22-2000002-2-12-1-2-2211−i3−i3i3i322-2-2-1−i3i30011−i3−i3i3i3-1-1100−i3−i3i3i3-1-1110000−2i2i−2i2i0000000000000000i−i−33i−i−330000
χ3722-2-22002-2-22-2000002-2-12-1-2-2211i3i3−i3−i322-2-2-1i3−i30011i3i3−i3−i3-1-1100i3i3−i3−i3-1-11100002i−2i2i−2i0000000000000000−ii−33−ii−330000
χ3822-2-22002-2-22-2000002-2-12-1-2-2211i3i3−i3−i322-2-2-1i3−i30011i3i3−i3−i3-1-1100i3i3−i3−i3-1-1110000−2i2i−2i2i0000000000000000i−i3−3i−i3−30000
χ3922-2-2200-22-22-200000-22222-2-22-2-20000-2-22220000-2-200002-22000000-2-22200002i−2i−2i2i00000000000000002i−2i00−2i2i000000
χ4022-2-2200-22-22-200000-22222-2-22-2-20000-2-22220000-2-200002-22000000-2-2220000−2i2i2i−2i0000000000000000−2i2i002i−2i000000
χ4122-2-2200-22-22-200000-22-12-1-2-2211−i3−i3i3i3-2-222-1i3−i30011i3i3−i3−i3-11-100−i3−i3i3i311-1-100002i−2i−2i2i0000000000000000−ii3−3i−i−330000
χ4222-2-2200-22-22-200000-22-12-1-2-2211−i3−i3i3i3-2-222-1i3−i30011i3i3−i3−i3-11-100−i3−i3i3i311-1-10000−2i2i2i−2i0000000000000000i−i−33−ii3−30000
χ4322-2-2200-22-22-200000-22-12-1-2-2211i3i3−i3−i3-2-222-1−i3i30011−i3−i3i3i3-11-100i3i3−i3−i311-1-100002i−2i−2i2i0000000000000000−ii−33i−i3−30000
χ4422-2-2200-22-22-200000-22-12-1-2-2211i3i3−i3−i3-2-222-1−i3i30011−i3−i3i3i3-11-100i3i3−i3−i311-1-10000−2i2i2i−2i0000000000000000i−i3−3−ii−330000
χ452-22-222i−2i002-2-20002i−2i0022-22-2-22-22i−2i2i−2i0000200002-20000-2002i−2i2i−2i2i−2i00002-22i−2i0000000000002-22i−2i0000000000000000
χ462-22-222i−2i002-2-20002i−2i0022-22-2-22-22i−2i2i−2i0000200002-20000-2002i−2i2i−2i2i−2i0000-22−2i2i000000000000-22−2i2i0000000000000000
χ472-22-222i−2i002-2-20002i−2i002-1-2-1112-22i−2i2i−2i3−33−3-100−i3i3-11−i3i3−i3i3100−ii−ii−ii3−33−32-22i−2i000000000000-11−ii−i3i33−3000000000000
χ482-22-222i−2i002-2-20002i−2i002-1-2-1112-22i−2i2i−2i3−33−3-100−i3i3-11−i3i3−i3i3100−ii−ii−ii3−33−3-22−2i2i0000000000001-1i−ii3−i3−33000000000000
χ492-22-222i−2i002-2-20002i−2i002-1-2-1112-22i−2i2i−2i−33−33-100i3−i3-11i3−i3i3−i3100−ii−ii−ii−33−332-22i−2i000000000000-11−iii3−i3−33000000000000
χ502-22-222i−2i002-2-20002i−2i002-1-2-1112-22i−2i2i−2i−33−33-100i3−i3-11i3−i3i3−i3100−ii−ii−ii−33−33-22−2i2i0000000000001-1i−i−i3i33−3000000000000
χ512-22-22−2i2i002-2-2000−2i2i0022-22-2-22-2−2i2i−2i2i0000200002-20000-200−2i2i−2i2i−2i2i00002-2−2i2i0000000000002-2−2i2i0000000000000000
χ522-22-22−2i2i002-2-2000−2i2i0022-22-2-22-2−2i2i−2i2i0000200002-20000-200−2i2i−2i2i−2i2i0000-222i−2i000000000000-222i−2i0000000000000000
χ532-22-22−2i2i002-2-2000−2i2i002-1-2-1112-2−2i2i−2i2i3−33−3-100i3−i3-11i3−i3i3−i3100i−ii−ii−i3−33−32-2−2i2i000000000000-11i−ii3−i33−3000000000000
χ542-22-22−2i2i002-2-2000−2i2i002-1-2-1112-2−2i2i−2i2i3−33−3-100i3−i3-11i3−i3i3−i3100i−ii−ii−i3−33−3-222i−2i0000000000001-1−ii−i3i3−33000000000000
χ552-22-22−2i2i002-2-2000−2i2i002-1-2-1112-2−2i2i−2i2i−33−33-100−i3i3-11−i3i3−i3i3100i−ii−ii−i−33−332-2−2i2i000000000000-11i−i−i3i3−33000000000000
χ562-22-22−2i2i002-2-2000−2i2i002-1-2-1112-2−2i2i−2i2i−33−33-100−i3i3-11−i3i3−i3i3100i−ii−ii−i−33−33-222i−2i0000000000001-1−iii3−i33−3000000000000
χ574444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-211111111000000000000000000000000000000000000
χ584444444-4-4444-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-222221222211-1-1-1-1122-2-21111-1-1-1-1000000000000000000000000000000000000
χ5944444-4-444444-4-4-4-4-444-2-2-2-2-2-2-2-22222-2-2-2-21222211-1-1-1-11-2-222-1-1-1-11111000000000000000000000000000000000000
χ6044444-4-4-4-4444444-4-4-4-4-2-2-2-2-2-2-2-2222222221-2-2-2-211111112222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ6144-4-44004-4-44-4000004-44-2422-2-4-40000-2-222-20000220000-24-4000000-2-222000000000000000000000000000000000000
χ6244-4-44004-4-44-4000004-4-2-2-222-222−2i3−2i32i32i3-2-2221−2i32i300-1-1i3i3−i3−i31-2200i3i3−i3−i311-1-1000000000000000000000000000000000000
χ6344-4-44004-4-44-4000004-4-2-2-222-2222i32i3−2i3−2i3-2-22212i3−2i300-1-1−i3−i3i3i31-2200−i3−i3i3i311-1-1000000000000000000000000000000000000
χ6444-4-4400-44-44-400000-444-2422-2-4-4000022-2-2-20000220000-2-4400000022-2-2000000000000000000000000000000000000
χ6544-4-4400-44-44-400000-44-2-2-222-222−2i3−2i32i32i322-2-212i3−2i300-1-1−i3−i3i3i312-200i3i3−i3−i3-1-111000000000000000000000000000000000000
χ6644-4-4400-44-44-400000-44-2-2-222-2222i32i3−2i3−2i322-2-21−2i32i300-1-1i3i3−i3−i312-200−i3−i3i3i3-1-111000000000000000000000000000000000000
χ674-44-444i−4i004-4-40004i−4i00-2424-4-4-22−2i2i−2i2i0000-20000-2200002004i−4i−2i2i−2i2i0000000000000000000000000000000000000000
χ684-44-444i−4i004-4-40004i−4i00-2-22-222-22−2i2i−2i2i23−2323−23100−2i32i31-1i3−i3i3−i3-100−2i2ii−ii−i−33−33000000000000000000000000000000000000
χ694-44-444i−4i004-4-40004i−4i00-2-22-222-22−2i2i−2i2i−2323−23231002i3−2i31-1−i3i3−i3i3-100−2i2ii−ii−i3−33−3000000000000000000000000000000000000
χ704-44-44−4i4i004-4-4000−4i4i00-2424-4-4-222i−2i2i−2i0000-20000-220000200−4i4i2i−2i2i−2i0000000000000000000000000000000000000000
χ714-44-44−4i4i004-4-4000−4i4i00-2-22-222-222i−2i2i−2i23−2323−231002i3−2i31-1−i3i3−i3i3-1002i−2i−ii−ii−33−33000000000000000000000000000000000000
χ724-44-44−4i4i004-4-4000−4i4i00-2-22-222-222i−2i2i−2i−2323−2323100−2i32i31-1i3−i3i3−i3-1002i−2i−ii−ii3−33−3000000000000000000000000000000000000
χ734-4-4440000-4-44000000044-4-44-4-440000000040000-440000-4000000000000000000000000000000000000000000000000
χ744-4-4440000-4-4400000004-2-42-22-44000023−23−2323-200002-2000020000000023−23−2323000000000000000000000000000000000000
χ754-4-4440000-4-4400000004-2-42-22-440000−232323−23-200002-20000200000000−232323−23000000000000000000000000000000000000
χ764-4-4440000-4-440000000-242-44-42-223−23−23230000-200002-200002000023−23−23230000000000000000000000000000000000000000
χ774-4-4440000-4-440000000-242-44-42-2−232323−230000-200002-2000020000−232323−230000000000000000000000000000000000000000
χ784-4-4440000-4-440000000-2-222-222-223−23−232323−23−232310000-11-333-3-10000−333−3−333−3000000000000000000000000000000000000
χ794-4-4440000-4-440000000-2-222-222-223−23−2323−232323−2310000-113-3-33-10000−333−33−3−33000000000000000000000000000000000000
χ804-4-4440000-4-440000000-2-222-222-2−232323−2323−23−232310000-113-3-33-100003−3−33−333−3000000000000000000000000000000000000
χ814-4-4440000-4-440000000-2-222-222-2−232323−23−232323−2310000-11-333-3-100003−3−333−3−33000000000000000000000000000000000000
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
χ846666-366-6-6-3-3-3-633-3-3330000000000000000000000000000000000000000000000002-200002-20000000000000000-11-11
χ856666-366-6-6-3-3-3-633-3-333000000000000000000000000000000000000000000000000-220000-2200000000000000001-11-1
χ866666-3-6-666-3-3-3-63333-3-3000000000000000000000000000000000000000000000000220000-2-20000000000000000-1-111
χ876666-3-6-666-3-3-3-63333-3-3000000000000000000000000000000000000000000000000-2-2000022000000000000000011-1-1
χ886666-3-6-6-6-6-3-3-36-3-333330000000000000000000000000000000000000000000000002-20000-220000000000000000-111-1
χ896666-3-6-6-6-6-3-3-36-3-33333000000000000000000000000000000000000000000000000-2200002-200000000000000001-1-11
χ901212-12-12-60012-126-6600000-660000000000000000000000000000000000000000000000000000000000000000000000000000
χ911212-12-12-600-12126-66000006-60000000000000000000000000000000000000000000000000000000000000000000000000000
χ9212-1212-12-612i−12i00-666000−6i6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-12-6−12i12i00-6660006i−6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-1212-6000066-60−6i36i300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-6000066-606i3−6i300000000000000000000000000000000000000000000000000000000000000000000000000000000

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