Finite Group Databasebeta

← Group #13147801

Character table — Group #13147801

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order1222344446664121212121212336666661212121212121212366612121212121212121212121212121212121212122222444444444444666612121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ51111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-1-11-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ71111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-111
χ81111111-1-1111-111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ911111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11111-11-11-1-11-111-1-111-1-111-1-111-1-11-11-1
χ1011111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11-111-11-1111-1-111-1-1-1-111-1-111-11-11
χ1111111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-11-1-11-1-111-1-11111-1-111-1-1-11-11
χ1211111-1-111111-1-1-111-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1111-1-1-111-1-111-1-111-1-1111-11-1
χ1311111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-11-1-1111-1-1-1-11111-1-1-1-1111-1-11
χ1411111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11-1111-111-1-1-1-111-1-11111-1-1-111-1
χ1511111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-11-111-1-11-1-1-11111-1-111-1-1-1-111-111-1
χ1611111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-11-11-11-11-1-11111-1-1-1-11111-1-11-1-11
χ1722222222222222222222-12-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222000000022000-1-1-1-1-1-1-1-1000000000000
χ1822222222222222222222-12-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000-2-200011111111000000000000
χ192222222222222222222-12-122-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022222000020000000000-1-1-1-1-1-1-1-10000
χ202222222222222222222-12-122-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2-20000-20000000000111111110000
χ212222222-2-2222-222-2-2-2-22-12-1-122-122221111-1-1-1-1-1-111-2-2-2-2-1-1-1-11111111122220000000-2-2000-1-1-1-11111000000000000
χ222222222-2-2222-222-2-2-2-22-12-1-122-122221111-1-1-1-1-1-111-2-2-2-2-1-1-1-111111111-2-2-2-20000000220001111-1-1-1-1000000000000
χ232222222-2-2222-222-2-2-2-2-12-122-1-12-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-111111111000022-2-2-2000020000000000-1-1-1-111110000
χ242222222-2-2222-222-2-2-2-2-12-122-1-12-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-1111111110000-2-22220000-200000000001111-1-1-1-10000
χ2522222-2-222222-2-2-222-2-22-12-1-122-1-2-2-2-2-1-1-1-1-1-1-1-1111122-2-21111-1-1-1-1111122-2-200000002-2000-1-111-1-111000000000000
χ2622222-2-222222-2-2-222-2-22-12-1-122-1-2-2-2-2-1-1-1-1-1-1-1-1111122-2-21111-1-1-1-11111-2-2220000000-2200011-1-111-1-1000000000000
χ2722222-2-222222-2-2-222-2-2-12-122-1-1211112222-1-1-1-1-2-2-2-2-1-1111111-1-1-1-1111100002222-20000-20000000000-1-111-1-1110000
χ2822222-2-222222-2-2-222-2-2-12-122-1-1211112222-1-1-1-1-2-2-2-2-1-1111111-1-1-1-111110000-2-2-2-2200002000000000011-1-111-1-10000
χ2922222-2-2-2-22222-2-2-2-2222-12-1-122-1-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-122-2-20000000-22000-1-11111-1-1000000000000
χ3022222-2-2-2-22222-2-2-2-2222-12-1-122-1-2-2-2-21111-1-1-1-111-1-1-2-22211111111-1-1-1-1-2-22200000002-200011-1-1-1-111000000000000
χ3122222-2-2-2-22222-2-2-2-222-12-122-1-121111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-1000022-2-220000-20000000000-1-11111-1-10000
χ3222222-2-2-2-22222-2-2-2-222-12-122-1-121111-2-2-2-2-1-1-1-1-2-22211-1-111111111-1-1-1-10000-2-222-200002000000000011-1-1-1-1110000
χ3322-2-222-2002-2-202-200002222-2-2-2-222-2-2000022-2-22-200000022-2-2000000002-22-20000000000002-22-20000000000000000
χ3422-2-222-2002-2-202-200002222-2-2-2-222-2-2000022-2-22-200000022-2-200000000-22-22000000000000-22-220000000000000000
χ3522-2-222-2002-2-202-200002-12-11-2-2122-2-233−3−3-1-111-113−30000-1-11133−3−333−3−32-22-2000000000000-11-113−33−3000000000000
χ3622-2-222-2002-2-202-200002-12-11-2-2122-2-233−3−3-1-111-113−30000-1-11133−3−333−3−3-22-220000000000001-11-1−33−33000000000000
χ3722-2-222-2002-2-202-200002-12-11-2-2122-2-2−3−333-1-111-11−330000-1-111−3−333−3−3332-22-2000000000000-11-11−33−33000000000000
χ3822-2-222-2002-2-202-200002-12-11-2-2122-2-2−3−333-1-111-11−330000-1-111−3−333−3−333-22-220000000000001-11-13−33−3000000000000
χ3922-2-22-22002-2-20-2200002222-2-2-2-2-2-222000022-2-2-22000000-2-222000000002-2-220000000000002-2-220000000000000000
χ4022-2-22-22002-2-20-2200002222-2-2-2-2-2-222000022-2-2-22000000-2-22200000000-222-2000000000000-222-20000000000000000
χ4122-2-22-22002-2-20-2200002-12-11-2-21-2-22233−3−3-1-1111-1−33000011-1-133−3−3−3−3332-2-22000000000000-111-13−3−33000000000000
χ4222-2-22-22002-2-20-2200002-12-11-2-21-2-22233−3−3-1-1111-1−33000011-1-133−3−3−3−333-222-20000000000001-1-11−333−3000000000000
χ4322-2-22-22002-2-20-2200002-12-11-2-21-2-222−3−333-1-1111-13−3000011-1-1−3−33333−3−32-2-22000000000000-111-1−333−3000000000000
χ4422-2-22-22002-2-20-2200002-12-11-2-21-2-222−3−333-1-1111-13−3000011-1-1−3−33333−3−3-222-20000000000001-1-113−3−33000000000000
χ452-22-22002i−2i-22-20002i−2i0022-2-222-2-200002i−2i2i−2i2-22-200002i−2i0000002i−2i2i−2i000000002-22i−2i00000000000000002-2002i−2i000000
χ462-22-22002i−2i-22-20002i−2i0022-2-222-2-200002i−2i2i−2i2-22-200002i−2i0000002i−2i2i−2i00000000-22−2i2i0000000000000000-2200−2i2i000000
χ472-22-22002i−2i-22-20002i−2i00-121-22-11-23−33−32i−2i2i−2i-11-110000−ii−i3i33−33−3−ii−ii−i3i3−i3i300002-22i−2i0000000000000000-113−3−ii−i3i30000
χ482-22-22002i−2i-22-20002i−2i00-121-22-11-23−33−32i−2i2i−2i-11-110000−ii−i3i33−33−3−ii−ii−i3i3−i3i30000-22−2i2i00000000000000001-1−33i−ii3−i30000
χ492-22-22002i−2i-22-20002i−2i00-121-22-11-2−33−332i−2i2i−2i-11-110000−iii3−i3−33−33−ii−iii3−i3i3−i300002-22i−2i0000000000000000-11−33−iii3−i30000
χ502-22-22002i−2i-22-20002i−2i00-121-22-11-2−33−332i−2i2i−2i-11-110000−iii3−i3−33−33−ii−iii3−i3i3−i30000-22−2i2i00000000000000001-13−3i−i−i3i30000
χ512-22-2200−2i2i-22-2000−2i2i0022-2-222-2-20000−2i2i−2i2i2-22-20000−2i2i000000−2i2i−2i2i000000002-2−2i2i00000000000000002-200−2i2i000000
χ522-22-2200−2i2i-22-2000−2i2i0022-2-222-2-20000−2i2i−2i2i2-22-20000−2i2i000000−2i2i−2i2i00000000-222i−2i0000000000000000-22002i−2i000000
χ532-22-2200−2i2i-22-2000−2i2i00-121-22-11-23−33−3−2i2i−2i2i-11-110000i−ii3−i33−33−3i−ii−ii3−i3i3−i300002-2−2i2i0000000000000000-113−3i−ii3−i30000
χ542-22-2200−2i2i-22-2000−2i2i00-121-22-11-23−33−3−2i2i−2i2i-11-110000i−ii3−i33−33−3i−ii−ii3−i3i3−i30000-222i−2i00000000000000001-1−33−ii−i3i30000
χ552-22-2200−2i2i-22-2000−2i2i00-121-22-11-2−33−33−2i2i−2i2i-11-110000i−i−i3i3−33−33i−ii−i−i3i3−i3i300002-2−2i2i0000000000000000-11−33i−i−i3i30000
χ562-22-2200−2i2i-22-2000−2i2i00-121-22-11-2−33−33−2i2i−2i2i-11-110000i−i−i3i3−33−33i−ii−i−i3i3−i3i30000-222i−2i00000000000000001-13−3−iii3−i30000
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
χ6144-4-444-4004-4-404-40000-24-24-422-4-2-2220000-2-2224-4000000-2-22200000000000000000000000000000000000000000000
χ6244-4-444-4004-4-404-40000-2-2-2-22222-2-2222323−23−2311-1-1-2223−23000011-1-1−3−333−3−333000000000000000000000000000000000000
χ6344-4-444-4004-4-404-40000-2-2-2-22222-2-222−23−23232311-1-1-22−2323000011-1-133−3−333−3−3000000000000000000000000000000000000
χ6444-4-44-44004-4-40-440000-24-24-422-422-2-20000-2-222-4400000022-2-200000000000000000000000000000000000000000000
χ6544-4-44-44004-4-40-440000-2-2-2-2222222-2-22323−23−2311-1-12-2−23230000-1-111−3−33333−3−3000000000000000000000000000000000000
χ6644-4-44-44004-4-40-440000-2-2-2-2222222-2-2−23−23232311-1-12-223−230000-1-11133−3−3−3−333000000000000000000000000000000000000
χ674-44-44004i−4i-44-40004i−4i004-2-42-24-420000−2i2i−2i2i-22-2200004i−4i000000−2i2i−2i2i0000000000000000000000000000000000000000
χ684-44-44004i−4i-44-40004i−4i00-2-222-2-22223−2323−23−2i2i−2i2i1-11-10000−2i2i−2i32i3−33−33i−ii−ii3−i3i3−i3000000000000000000000000000000000000
χ694-44-44004i−4i-44-40004i−4i00-2-222-2-222−2323−2323−2i2i−2i2i1-11-10000−2i2i2i3−2i33−33−3i−ii−i−i3i3−i3i3000000000000000000000000000000000000
χ704-44-4400−4i4i-44-4000−4i4i004-2-42-24-4200002i−2i2i−2i-22-220000−4i4i0000002i−2i2i−2i0000000000000000000000000000000000000000
χ714-44-4400−4i4i-44-4000−4i4i00-2-222-2-22223−2323−232i−2i2i−2i1-11-100002i−2i2i3−2i3−33−33−ii−ii−i3i3−i3i3000000000000000000000000000000000000
χ724-44-4400−4i4i-44-4000−4i4i00-2-222-2-222−2323−23232i−2i2i−2i1-11-100002i−2i−2i32i33−33−3−ii−iii3−i3i3−i3000000000000000000000000000000000000
χ734-4-4440000-4-44000000044-4-4-4-444000000004-4-4400000000000000000000000000000000000000000000000000000000
χ744-4-4440000-4-4400000004-2-422-44-20000−2i32i32i3−2i3-222-2000000000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ754-4-4440000-4-4400000004-2-422-44-200002i3−2i3−2i32i3-222-20000000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ764-4-4440000-4-440000000-242-4-42-2423−23−23230000-222-20000000023−23−232300000000000000000000000000000000000000000000
χ774-4-4440000-4-440000000-242-4-42-24−232323−230000-222-200000000−232323−2300000000000000000000000000000000000000000000
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
χ826666-36666-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000022000220000000000000000-1-1-1-1
χ836666-36666-3-3-36-3-3-3-3-3-30000000000000000000000000000000000000000000000000-2-2000-2-200000000000000001111
χ846666-366-6-6-3-3-3-6-3-33333000000000000000000000000000000000000000000000000022000-2-20000000000000000-1-111
χ856666-366-6-6-3-3-3-6-3-333330000000000000000000000000000000000000000000000000-2-200022000000000000000011-1-1
χ866666-3-6-666-3-3-3-633-3-33300000000000000000000000000000000000000000000000002-20002-20000000000000000-11-11
χ876666-3-6-666-3-3-3-633-3-3330000000000000000000000000000000000000000000000000-22000-2200000000000000001-11-1
χ886666-3-6-6-6-6-3-3-363333-3-300000000000000000000000000000000000000000000000002-2000-220000000000000000-111-1
χ896666-3-6-6-6-6-3-3-363333-3-30000000000000000000000000000000000000000000000000-220002-200000000000000001-1-11
χ901212-12-12-612-1200-6660-6600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ911212-12-12-6-121200-66606-600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9212-1212-12-60012i−12i6-66000−6i6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-12-600−12i12i6-660006i−6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-1212-6000066-60000063−630000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-6000066-600000−63630000000000000000000000000000000000000000000000000000000000000000000000000000

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