Finite Group Databasebeta

← Group #13147840

Character table — Group #13147840

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order122234444666412121212121233666666121212121212121236661212121212121212121212121212121212121212224444442224444466666666121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-11-1-11111-1-1-1-1-1-111-1-1111111-1-1
χ61111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-111-1-1111111-1-1-1-1-1-1-1-111
χ71111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-111
χ81111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-111-1-1111111-1-111-1-1-1-111-1-1
χ911111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-1-11-11-111-1-111-1-1-1-11111-1-11-11-1
χ1011111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11-1-11-1111-1-1-1-111-1-111-1-111-11-11
χ1111111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-11-11-11-1-11111-1-111-1-111-1-1-11-11
χ1211111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1111-11-1-1-111-1-11111-1-1-1-1111-11-1
χ1311111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-11-11-1-111-11111-1-111-1-1-1-111-1-11-1-11
χ1411111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11-1-11111111-1-1-1-1-1-1-1-111-111-1
χ1511111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-11-1-1-1-1-1-111111111-1-1-111-1
χ1611111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11-11-111-1-1-1-1-111-1-11111-1-1111-1-11
χ1722222222222222222222-122-1-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100002222022000000000-1-1-1-10000-1-1-1-10000
χ1822222222222222222222-122-1-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-20-2-20000000001111000011110000
χ192222222222222222222-12-1-122-12-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222000020020000-1-1-1-10000-1-1-1-100000000
χ202222222222222222222-12-1-122-12-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-200-2000011110000111100000000
χ212222222-2-2222-222-2-2-2-22-122-1-12-122221111-1-1-1-1-1-1-2-2-2-211-1-1-1-111111111000022220-2-200000000011110000-1-1-1-10000
χ222222222-2-2222-222-2-2-2-22-122-1-12-122221111-1-1-1-1-1-1-2-2-2-211-1-1-1-1111111110000-2-2-2-2022000000000-1-1-1-1000011110000
χ232222222-2-2222-222-2-2-2-2-12-1-122-12-1-1-1-1-2-2-2-2-1-1-1-1221111-2-2-1-1-1-11111111122-2-20000-20020000-1-1110000-1-11100000000
χ242222222-2-2222-222-2-2-2-2-12-1-122-12-1-1-1-1-2-2-2-2-1-1-1-1221111-2-2-1-1-1-111111111-2-2220000200-2000011-1-1000011-1-100000000
χ2522222-2-222222-2-2-222-2-22-122-1-12-1-2-2-2-2-1-1-1-1-1-1-1-11122-2-2111111-1-1-1-11111000022-2-202-2000000000-1-1110000-1-1110000
χ2622222-2-222222-2-2-222-2-22-122-1-12-1-2-2-2-2-1-1-1-1-1-1-1-11122-2-2111111-1-1-1-111110000-2-2220-2200000000011-1-1000011-1-10000
χ2722222-2-222222-2-2-222-2-2-12-1-122-1211112222-1-1-1-1-2-2-1-111-2-21111-1-1-1-1111122220000-200-20000-1-111000011-1-100000000
χ2822222-2-222222-2-2-222-2-2-12-1-122-1211112222-1-1-1-1-2-2-1-111-2-21111-1-1-1-11111-2-2-2-200002002000011-1-10000-1-11100000000
χ2922222-2-2-2-22222-2-2-2-2222-122-1-12-1-2-2-2-21111-1-1-1-111-2-222-1-111111111-1-1-1-1000022-2-20-2200000000011-1-10000-1-1110000
χ3022222-2-2-2-22222-2-2-2-2222-122-1-12-1-2-2-2-21111-1-1-1-111-2-222-1-111111111-1-1-1-10000-2-22202-2000000000-1-111000011-1-10000
χ3122222-2-2-2-22222-2-2-2-222-12-1-122-121111-2-2-2-2-1-1-1-1-2-211-1-12211111111-1-1-1-122-2-20000200-20000-1-1-1-10000111100000000
χ3222222-2-2-2-22222-2-2-2-222-12-1-122-121111-2-2-2-2-1-1-1-1-2-211-1-12211111111-1-1-1-1-2-2220000-2002000011110000-1-1-1-100000000
χ3322-2-22002i−2i-22-20002i−2i00222-22-2-2-200002i2i−2i−2i22-2-2002i−2i000000002i2i−2i−2i00002-22i−2i0000000000002-2000000002i−2i00000000
χ3422-2-22002i−2i-22-20002i−2i00222-22-2-2-200002i2i−2i−2i22-2-2002i−2i000000002i2i−2i−2i0000-22−2i2i000000000000-2200000000−2i2i00000000
χ3522-2-22002i−2i-22-20002i−2i00-12-112-21-233−3−32i2i−2i−2i-1-11100−ii−i3i30033−3−3−i−iii−i3−i3i3i32-22i−2i000000000000-11−i3i300003−3−ii00000000
χ3622-2-22002i−2i-22-20002i−2i00-12-112-21-233−3−32i2i−2i−2i-1-11100−ii−i3i30033−3−3−i−iii−i3−i3i3i3-22−2i2i0000000000001-1i3−i30000−33i−i00000000
χ3722-2-22002i−2i-22-20002i−2i00-12-112-21-2−3−3332i2i−2i−2i-1-11100−iii3−i300−3−333−i−iiii3i3−i3−i32-22i−2i000000000000-11i3−i30000−33−ii00000000
χ3822-2-22002i−2i-22-20002i−2i00-12-112-21-2−3−3332i2i−2i−2i-1-11100−iii3−i300−3−333−i−iiii3i3−i3−i3-22−2i2i0000000000001-1−i3i300003−3i−i00000000
χ3922-2-2200−2i2i-22-2000−2i2i00222-22-2-2-20000−2i−2i2i2i22-2-200−2i2i00000000−2i−2i2i2i00002-2−2i2i0000000000002-200000000−2i2i00000000
χ4022-2-2200−2i2i-22-2000−2i2i00222-22-2-2-20000−2i−2i2i2i22-2-200−2i2i00000000−2i−2i2i2i0000-222i−2i000000000000-22000000002i−2i00000000
χ4122-2-2200−2i2i-22-2000−2i2i00-12-112-21-233−3−3−2i−2i2i2i-1-11100i−ii3−i30033−3−3ii−i−ii3i3−i3−i32-2−2i2i000000000000-11i3−i300003−3i−i00000000
χ4222-2-2200−2i2i-22-2000−2i2i00-12-112-21-233−3−3−2i−2i2i2i-1-11100i−ii3−i30033−3−3ii−i−ii3i3−i3−i3-222i−2i0000000000001-1−i3i30000−33−ii00000000
χ4322-2-2200−2i2i-22-2000−2i2i00-12-112-21-2−3−333−2i−2i2i2i-1-11100i−i−i3i300−3−333ii−i−i−i3−i3i3i32-2−2i2i000000000000-11−i3i30000−33i−i00000000
χ4422-2-2200−2i2i-22-2000−2i2i00-12-112-21-2−3−333−2i−2i2i2i-1-11100i−i−i3i300−3−333ii−i−i−i3−i3i3i3-222i−2i0000000000001-1i3−i300003−3−ii00000000
χ452-22-222-2002-2-202-2000022-2-2-222-22-22-200002-22-22-20000002-22-20000000000002i−2i2i−2i000000000000000000002i−2i2i−2i0000
χ462-22-222-2002-2-202-2000022-2-2-222-22-22-200002-22-22-20000002-22-2000000000000−2i2i−2i2i00000000000000000000−2i2i−2i2i0000
χ472-22-222-2002-2-202-200002-1-2-21-1212-22-23−33−3-11-11-1100003−3-11-113−33−33−33−300002i−2i2i−2i000000000000−i3i3−i3i30000−ii−ii0000
χ482-22-222-2002-2-202-200002-1-2-21-1212-22-23−33−3-11-11-1100003−3-11-113−33−33−33−30000−2i2i−2i2i000000000000i3−i3i3−i30000i−ii−i0000
χ492-22-222-2002-2-202-200002-1-2-21-1212-22-2−33−33-11-11-110000−33-11-11−33−33−33−3300002i−2i2i−2i000000000000i3−i3i3−i30000−ii−ii0000
χ502-22-222-2002-2-202-200002-1-2-21-1212-22-2−33−33-11-11-110000−33-11-11−33−33−33−330000−2i2i−2i2i000000000000−i3i3−i3i30000i−ii−i0000
χ512-22-22-22002-2-20-22000022-2-2-222-2-22-2200002-22-2-22000000-22-220000000000002i−2i−2i2i000000000000000000002i−2i−2i2i0000
χ522-22-22-22002-2-20-22000022-2-2-222-2-22-2200002-22-2-22000000-22-22000000000000−2i2i2i−2i00000000000000000000−2i2i2i−2i0000
χ532-22-22-22002-2-20-2200002-1-2-21-121-22-223−33−3-11-111-10000−331-11-13−33−3−33−3300002i−2i−2i2i000000000000−i3i3i3−i30000−iii−i0000
χ542-22-22-22002-2-20-2200002-1-2-21-121-22-223−33−3-11-111-10000−331-11-13−33−3−33−330000−2i2i2i−2i000000000000i3−i3−i3i30000i−i−ii0000
χ552-22-22-22002-2-20-2200002-1-2-21-121-22-22−33−33-11-111-100003−31-11-1−33−333−33−300002i−2i−2i2i000000000000i3−i3−i3i30000−iii−i0000
χ562-22-22-22002-2-20-2200002-1-2-21-121-22-22−33−33-11-111-100003−31-11-1−33−333−33−30000−2i2i2i−2i000000000000−i3i3i3−i30000i−i−ii0000
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−4i-44-40004i−4i004-24-4-22-420000−2i−2i2i2i-2-222004i−4i00000000−2i−2i2i2i0000000000000000000000000000000000000000
χ6244-4-44004i−4i-44-40004i−4i00-2-2-22-22222323−23−23−2i−2i2i2i11-1-100−2i2i−2i32i300−3−333ii−i−ii3i3−i3−i3000000000000000000000000000000000000
χ6344-4-44004i−4i-44-40004i−4i00-2-2-22-2222−23−232323−2i−2i2i2i11-1-100−2i2i2i3−2i30033−3−3ii−i−i−i3−i3i3i3000000000000000000000000000000000000
χ6444-4-4400−4i4i-44-4000−4i4i004-24-4-22-4200002i2i−2i−2i-2-22200−4i4i000000002i2i−2i−2i0000000000000000000000000000000000000000
χ6544-4-4400−4i4i-44-4000−4i4i00-2-2-22-22222323−23−232i2i−2i−2i11-1-1002i−2i2i3−2i300−3−333−i−iii−i3−i3i3i3000000000000000000000000000000000000
χ6644-4-4400−4i4i-44-4000−4i4i00-2-2-22-2222−23−2323232i2i−2i−2i11-1-1002i−2i−2i32i30033−3−3−i−iiii3i3−i3−i3000000000000000000000000000000000000
χ674-44-444-4004-4-404-40000-2422-44-2-4-22-220000-22-224-4000000-22-2200000000000000000000000000000000000000000000
χ684-44-444-4004-4-404-40000-2-2222-2-22-22-2223−2323−231-11-1-22000023−231-11-1−33−33−33−33000000000000000000000000000000000000
χ694-44-444-4004-4-404-40000-2-2222-2-22-22-22−2323−23231-11-1-220000−23231-11-13−33−33−33−3000000000000000000000000000000000000
χ704-44-44-44004-4-40-440000-2422-44-2-42-22-20000-22-22-440000002-22-200000000000000000000000000000000000000000000
χ714-44-44-44004-4-40-440000-2-2222-2-222-22-223−2323−231-11-12-20000−2323-11-11−33−333−33−3000000000000000000000000000000000000
χ724-44-44-44004-4-40-440000-2-2222-2-222-22-2−2323−23231-11-12-2000023−23-11-113−33−3−33−33000000000000000000000000000000000000
χ734-4-4440000-4-44000000044-44-4-4-44000000004-4-4400000000000000000000000000000000000000000000000000000000
χ744-4-4440000-4-4400000004-2-4422-4-20000−2i32i32i3−2i3-222-2000000000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ754-4-4440000-4-4400000004-2-4422-4-200002i3−2i3−2i32i3-222-20000000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ764-4-4440000-4-440000000-242-2-4-42423−23−23230000-222-20000000023−23−232300000000000000000000000000000000000000000000
χ774-4-4440000-4-440000000-242-2-4-424−232323−230000-222-200000000−232323−2300000000000000000000000000000000000000000000
χ784-4-4440000-4-440000000-2-22-2222-223−23−2323−2i32i32i3−2i31-1-1100000000−333−3i3−i3−i3i33i−3i−3i3i000000000000000000000000000000000000
χ794-4-4440000-4-440000000-2-22-2222-223−23−23232i3−2i3−2i32i31-1-1100000000−333−3−i3i3i3−i3−3i3i3i−3i000000000000000000000000000000000000
χ804-4-4440000-4-440000000-2-22-2222-2−232323−23−2i32i32i3−2i31-1-11000000003−3−33i3−i3−i3i3−3i3i3i−3i000000000000000000000000000000000000
χ814-4-4440000-4-440000000-2-22-2222-2−232323−232i3−2i3−2i32i31-1-11000000003−3−33−i3i3i3−i33i−3i−3i3i000000000000000000000000000000000000
χ826666-36666-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000000022220000000000000000-1-1-1-1
χ836666-36666-3-3-36-3-3-3-3-3-30000000000000000000000000000000000000000000000000000-2-2-2-200000000000000001111
χ846666-366-6-6-3-3-3-6-3-33333000000000000000000000000000000000000000000000000000022-2-2000000000000000011-1-1
χ856666-366-6-6-3-3-3-6-3-333330000000000000000000000000000000000000000000000000000-2-2220000000000000000-1-111
χ866666-3-6-666-3-3-3-633-3-33300000000000000000000000000000000000000000000000000002-22-20000000000000000-11-11
χ876666-3-6-666-3-3-3-633-3-3330000000000000000000000000000000000000000000000000000-22-2200000000000000001-11-1
χ886666-3-6-6-6-6-3-3-363333-3-300000000000000000000000000000000000000000000000000002-2-2200000000000000001-1-11
χ896666-3-6-6-6-6-3-3-363333-3-30000000000000000000000000000000000000000000000000000-222-20000000000000000-111-1
χ901212-12-12-60012i−12i6-66000−6i6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ911212-12-12-600−12i12i6-660006i−6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9212-1212-12-612-1200-6660-6600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-12-6-121200-66606-600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-1212-6000066-60000063−630000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-6000066-600000−63630000000000000000000000000000000000000000000000000000000000000000000000000000

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