Finite Group Databasebeta

← Group #13147862

Character table — Group #13147862

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order12223444466641212121212123366666612121212121212123666121212121212121212121212121212121212121244444444224444446612121212121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-11-1-11-11-1-1-11111-1-11111-1-1-1-111-1-1
χ61111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11-1-11-11-1-11111-1-1-1-1-1-11111-1-111
χ71111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1111-1-1111-1-1-1-1111111-1-1-1-1-1-111
χ81111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-111-111-1-1-1-111-1-1-1-1111111-1-1
χ911111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-11-1-111-1-111-1-11111-1-111-1-1-111-1
χ1011111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-111-1-111-1-111-1-1111-1-11
χ1111111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111111-1-1-1-1-111-1-111-1-111-1-111-1-11-1-11
χ1211111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-1-1-1111111-1-111-1-1-1-111-1-111-111-1
χ1311111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-11-11-1-111-11111-1-1-1-111-1-1-1-111-11-11
χ1411111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11-1-111111-1-1-1-1-1-11111-1-11-11-1
χ1511111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-11-11-11-11-1-1-1-1111111-1-1-1-1111-11-1
χ1611111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1111-11-1-1-1-1-11111-1-11111-1-1-11-11
χ1722222222222222222222-12-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222000020020000-1-1-1-1-1-1-1-1000000000000
χ1822222222222222222222-12-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-200-2000011111111000000000000
χ192222222222222222222-12-1222-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022220000220000000000-1-1-1-1-1-1-1-10000
χ202222222222222222222-12-1222-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-20000-2-20000000000111111110000
χ212222222-2-2222-222-2-2-2-22-12-1-1-12222221111-1-1-1-1-1-111-2-2-2-2-1-1-1-11111111122220000-200-2000011-1-1-1-111000000000000
χ222222222-2-2222-222-2-2-2-22-12-1-1-12222221111-1-1-1-1-1-111-2-2-2-2-1-1-1-111111111-2-2-2-2000020020000-1-11111-1-1000000000000
χ232222222-2-2222-222-2-2-2-2-12-1222-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-111111111000022-2-200002-20000000000-1-1-1-111110000
χ242222222-2-2222-222-2-2-2-2-12-1222-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-1111111110000-2-2220000-2200000000001111-1-1-1-10000
χ2522222-2-222222-2-2-222-2-22-12-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1111122-2-21111-1-1-1-1111122-2-20000-2002000011-1-111-1-1000000000000
χ2622222-2-222222-2-2-222-2-22-12-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1111122-2-21111-1-1-1-11111-2-2220000200-20000-1-111-1-111000000000000
χ2722222-2-222222-2-2-222-2-2-12-1222-1-111112222-1-1-1-1-2-2-2-2-1-1111111-1-1-1-11111000022220000-2-20000000000-1-111-1-1110000
χ2822222-2-222222-2-2-222-2-2-12-1222-1-111112222-1-1-1-1-2-2-2-2-1-1111111-1-1-1-111110000-2-2-2-2000022000000000011-1-111-1-10000
χ2922222-2-2-2-22222-2-2-2-2222-12-1-1-122-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-122-2-20000200-20000-1-1-1-11111000000000000
χ3022222-2-2-2-22222-2-2-2-2222-12-1-1-122-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-1-2-2220000-200200001111-1-1-1-1000000000000
χ3122222-2-2-2-22222-2-2-2-222-12-1222-1-11111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-1000022-2-20000-220000000000-1-11111-1-10000
χ3222222-2-2-2-22222-2-2-2-222-12-1222-1-11111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-10000-2-22200002-2000000000011-1-1-1-1110000
χ332-22-22002i−2i2-2-20002i−2i0022-22-2-22-200002i2i−2i−2i22-2-200002i−2i0000002i2i−2i−2i000000002i−2i2-200000000000000002i−2i002-2000000
χ342-22-22002i−2i2-2-20002i−2i0022-22-2-22-200002i2i−2i−2i22-2-200002i−2i0000002i2i−2i−2i00000000−2i2i-220000000000000000−2i2i00-22000000
χ352-22-22002i−2i2-2-20002i−2i00-1212-2-2-1133−3−32i2i−2i−2i-1-1110000−ii−i3i333−3−3−i−iii−i3−i3i3i300002i−2i2-20000000000000000−ii−i3i3-113−30000
χ362-22-22002i−2i2-2-20002i−2i00-1212-2-2-1133−3−32i2i−2i−2i-1-1110000−ii−i3i333−3−3−i−iii−i3−i3i3i30000−2i2i-220000000000000000i−ii3−i31-1−330000
χ372-22-22002i−2i2-2-20002i−2i00-1212-2-2-11−3−3332i2i−2i−2i-1-1110000−iii3−i3−3−333−i−iiii3i3−i3−i300002i−2i2-20000000000000000−iii3−i3-11−330000
χ382-22-22002i−2i2-2-20002i−2i00-1212-2-2-11−3−3332i2i−2i−2i-1-1110000−iii3−i3−3−333−i−iiii3i3−i3−i30000−2i2i-220000000000000000i−i−i3i31-13−30000
χ392-22-2200−2i2i2-2-2000−2i2i0022-22-2-22-20000−2i−2i2i2i22-2-20000−2i2i000000−2i−2i2i2i000000002i−2i-2200000000000000002i−2i00-22000000
χ402-22-2200−2i2i2-2-2000−2i2i0022-22-2-22-20000−2i−2i2i2i22-2-20000−2i2i000000−2i−2i2i2i00000000−2i2i2-20000000000000000−2i2i002-2000000
χ412-22-2200−2i2i2-2-2000−2i2i00-1212-2-2-1133−3−3−2i−2i2i2i-1-1110000i−ii3−i333−3−3ii−i−ii3i3−i3−i300002i−2i-220000000000000000−ii−i3i31-1−330000
χ422-22-2200−2i2i2-2-2000−2i2i00-1212-2-2-1133−3−3−2i−2i2i2i-1-1110000i−ii3−i333−3−3ii−i−ii3i3−i3−i30000−2i2i2-20000000000000000i−ii3−i3-113−30000
χ432-22-2200−2i2i2-2-2000−2i2i00-1212-2-2-11−3−333−2i−2i2i2i-1-1110000i−i−i3i3−3−333ii−i−i−i3−i3i3i300002i−2i-220000000000000000−iii3−i31-13−30000
χ442-22-2200−2i2i2-2-2000−2i2i00-1212-2-2-11−3−333−2i−2i2i2i-1-1110000i−i−i3i3−3−333ii−i−i−i3−i3i3i30000−2i2i2-20000000000000000i−i−i3i3-11−330000
χ452-2-2222i−2i00-22-202i−2i000022-2-22-2-222i−2i2i−2i00002-22-22i−2i0000002i−2i2i−2i000000002i−2i2-2000000000000002i−2i2-200000000000000
χ462-2-2222i−2i00-22-202i−2i000022-2-22-2-222i−2i2i−2i00002-22-22i−2i0000002i−2i2i−2i00000000−2i2i-2200000000000000−2i2i-2200000000000000
χ472-2-2222i−2i00-22-202i−2i00002-1-21-11-222i−2i2i−2i−i3i3−i3i3-11-11−ii3−30000−ii−ii−i3i3−i3i33−33−32i−2i2-2000000000000−i3i3−ii-113−3000000000000
χ482-2-2222i−2i00-22-202i−2i00002-1-21-11-222i−2i2i−2i−i3i3−i3i3-11-11−ii3−30000−ii−ii−i3i3−i3i33−33−3−2i2i-22000000000000i3−i3i−i1-1−33000000000000
χ492-2-2222i−2i00-22-202i−2i00002-1-21-11-222i−2i2i−2ii3−i3i3−i3-11-11−ii−330000−ii−iii3−i3i3−i3−33−332i−2i2-2000000000000i3−i3−ii-11−33000000000000
χ502-2-2222i−2i00-22-202i−2i00002-1-21-11-222i−2i2i−2ii3−i3i3−i3-11-11−ii−330000−ii−iii3−i3i3−i3−33−33−2i2i-22000000000000−i3i3i−i1-13−3000000000000
χ512-2-222−2i2i00-22-20−2i2i000022-2-22-2-22−2i2i−2i2i00002-22-2−2i2i000000−2i2i−2i2i000000002i−2i-22000000000000002i−2i-2200000000000000
χ522-2-222−2i2i00-22-20−2i2i000022-2-22-2-22−2i2i−2i2i00002-22-2−2i2i000000−2i2i−2i2i00000000−2i2i2-200000000000000−2i2i2-200000000000000
χ532-2-222−2i2i00-22-20−2i2i00002-1-21-11-22−2i2i−2i2i−i3i3−i3i3-11-11i−i−330000i−ii−i−i3i3−i3i3−33−332i−2i-22000000000000i3−i3−ii1-13−3000000000000
χ542-2-222−2i2i00-22-20−2i2i00002-1-21-11-22−2i2i−2i2i−i3i3−i3i3-11-11i−i−330000i−ii−i−i3i3−i3i3−33−33−2i2i2-2000000000000−i3i3i−i-11−33000000000000
χ552-2-222−2i2i00-22-20−2i2i00002-1-21-11-22−2i2i−2i2ii3−i3i3−i3-11-11i−i3−30000i−ii−ii3−i3i3−i33−33−32i−2i-22000000000000−i3i3−ii1-1−33000000000000
χ562-2-222−2i2i00-22-20−2i2i00002-1-21-11-22−2i2i−2i2ii3−i3i3−i3-11-11i−i3−30000i−ii−ii3−i3i3−i33−33−3−2i2i2-2000000000000i3−i3i−i-113−3000000000000
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
χ6144-4-440000-4-440000000444-4-44-4-4000000004-4-4400000000000000000000000000000000000000000000000000000000
χ6244-4-440000-4-4400000004-2422-2-4-4000023−23−2323-222-200000000000023−23−23230000000000000000000000000000000000000000
χ6344-4-440000-4-4400000004-2422-2-4-40000−232323−23-222-2000000000000−232323−230000000000000000000000000000000000000000
χ6444-4-440000-4-440000000-24-2-4-4422−2i32i32i3−2i30000-222-200000000−2i32i32i3−2i300000000000000000000000000000000000000000000
χ6544-4-440000-4-440000000-24-2-4-44222i3−2i3−2i32i30000-222-2000000002i3−2i3−2i32i300000000000000000000000000000000000000000000
χ6644-4-440000-4-440000000-2-2-222-222−2i32i32i3−2i323−23−23231-1-1100000000i3−i3−i3i3−333−33i−3i−3i3i000000000000000000000000000000000000
χ6744-4-440000-4-440000000-2-2-222-222−2i32i32i3−2i3−232323−231-1-1100000000i3−i3−i3i33−3−33−3i3i3i−3i000000000000000000000000000000000000
χ6844-4-440000-4-440000000-2-2-222-2222i3−2i3−2i32i323−23−23231-1-1100000000−i3i3i3−i3−333−3−3i3i3i−3i000000000000000000000000000000000000
χ6944-4-440000-4-440000000-2-2-222-2222i3−2i3−2i32i3−232323−231-1-1100000000−i3i3i3−i33−3−333i−3i−3i3i000000000000000000000000000000000000
χ704-44-44004i−4i4-4-40004i−4i004-2-4-2224-40000−2i−2i2i2i-2-22200004i−4i000000−2i−2i2i2i0000000000000000000000000000000000000000
χ714-44-44004i−4i4-4-40004i−4i00-2-22-222-222323−23−23−2i−2i2i2i11-1-10000−2i2i−2i32i3−3−333ii−i−ii3i3−i3−i3000000000000000000000000000000000000
χ724-44-44004i−4i4-4-40004i−4i00-2-22-222-22−23−232323−2i−2i2i2i11-1-10000−2i2i2i3−2i333−3−3ii−i−i−i3−i3i3i3000000000000000000000000000000000000
χ734-44-4400−4i4i4-4-4000−4i4i004-2-4-2224-400002i2i−2i−2i-2-2220000−4i4i0000002i2i−2i−2i0000000000000000000000000000000000000000
χ744-44-4400−4i4i4-4-4000−4i4i00-2-22-222-222323−23−232i2i−2i−2i11-1-100002i−2i2i3−2i3−3−333−i−iii−i3−i3i3i3000000000000000000000000000000000000
χ754-44-4400−4i4i4-4-4000−4i4i00-2-22-222-22−23−2323232i2i−2i−2i11-1-100002i−2i−2i32i333−3−3−i−iiii3i3−i3−i3000000000000000000000000000000000000
χ764-4-4444i−4i00-44-404i−4i0000-242-44-42-2−2i2i−2i2i0000-22-224i−4i000000−2i2i−2i2i00000000000000000000000000000000000000000000
χ774-4-4444i−4i00-44-404i−4i0000-2-222-222-2−2i2i−2i2i−2i32i3−2i32i31-11-1−2i2i23−230000i−ii−ii3−i3i3−i3−33−33000000000000000000000000000000000000
χ784-4-4444i−4i00-44-404i−4i0000-2-222-222-2−2i2i−2i2i2i3−2i32i3−2i31-11-1−2i2i−23230000i−ii−i−i3i3−i3i33−33−3000000000000000000000000000000000000
χ794-4-444−4i4i00-44-40−4i4i0000-242-44-42-22i−2i2i−2i0000-22-22−4i4i0000002i−2i2i−2i00000000000000000000000000000000000000000000
χ804-4-444−4i4i00-44-40−4i4i0000-2-222-222-22i−2i2i−2i−2i32i3−2i32i31-11-12i−2i−23230000−ii−iii3−i3i3−i33−33−3000000000000000000000000000000000000
χ814-4-444−4i4i00-44-40−4i4i0000-2-222-222-22i−2i2i−2i2i3−2i32i3−2i31-11-12i−2i23−230000−ii−ii−i3i3−i3i3−33−33000000000000000000000000000000000000
χ826666-36666-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000022000220000000000000000-1-1-1-1
χ836666-36666-3-3-36-3-3-3-3-3-30000000000000000000000000000000000000000000000000-2-2000-2-200000000000000001111
χ846666-366-6-6-3-3-3-6-3-3333300000000000000000000000000000000000000000000000002-20002-20000000000000000-1-111
χ856666-366-6-6-3-3-3-6-3-333330000000000000000000000000000000000000000000000000-22000-22000000000000000011-1-1
χ866666-3-6-666-3-3-3-633-3-333000000000000000000000000000000000000000000000000022000-2-20000000000000000-111-1
χ876666-3-6-666-3-3-3-633-3-3330000000000000000000000000000000000000000000000000-2-20002200000000000000001-1-11
χ886666-3-6-6-6-6-3-3-363333-3-300000000000000000000000000000000000000000000000002-2000-220000000000000000-11-11
χ896666-3-6-6-6-6-3-3-363333-3-30000000000000000000000000000000000000000000000000-220002-200000000000000001-11-1
χ901212-12-12-6000066-60000063−630000000000000000000000000000000000000000000000000000000000000000000000000000
χ911212-12-12-6000066-600000−63630000000000000000000000000000000000000000000000000000000000000000000000000000
χ9212-1212-12-60012i−12i-666000−6i6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-12-600−12i12i-6660006i−6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-1212-612i−12i006-660−6i6i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-6−12i12i006-6606i−6i00000000000000000000000000000000000000000000000000000000000000000000000000000000

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