Finite Group Databasebeta

← Group #13147828

Character table — Group #13147828

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order1222344446661212121241212121233666666121212123666121212121212121212121212121212121212121212122244444424444444666612121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1
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
χ51111111-1-11111111-1-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-1111111-1-1-1-111-1-1-1-111-1-1
χ61111111-1-11111111-1-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-11-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111
χ71111111-1-11111111-1-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1-11111-1-111-1-1-1-1-1-11111-1-111
χ81111111-1-11111111-1-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111111-1-1-1-1-1-1-1-11111-1-1111111-1-1
χ911111-1-111111-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-11-11-11-1-1-1111111-1-1-1-111-1-11-11-1
χ1011111-1-111111-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111-1-11-111111-1-1-1-111-1-111-1-1-11-11
χ1111111-1-111111-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-11-11-11-1-1-1-11111-1-111-1-111-11-11
χ1211111-1-111111-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-111-11-111-1-1-1-1-1-11111-1-1111-11-1
χ1311111-1-1-1-1111-1-1-1-11-1-11111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-11-111-1-11-1-11111-1-111-1-1-1-1111-1-11
χ1411111-1-1-1-1111-1-1-1-11-1-11111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11-111-11111-1-111-1-1-1-1-1-111-111-1
χ1511111-1-1-1-1111-1-1-1-11-1-11111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1-111-1-1-1-1-111-1-1111111-1-1-111-1
χ1611111-1-1-1-1111-1-1-1-11-1-11111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111-11-11-1-1111-1-1-1-111-1-11111-1-11-1-11
χ172222222222222222222222-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222200000022000000-1-1000000-1-1-1-1-1-10000
χ182222222222222222222222-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000-2-2000000110000001111110000
χ19222222222222222222222-12-1222-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022220000000000000000-1-1-1-1
χ20222222222222222222222-12-1222-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-200000000000000001111
χ212222222-2-22222222-2-2-2-2-22-12-1-1-1221111-1-1-1-1-2-2-1-11122-2-2-1-1-1-1111111112222000000-2-2000000-1-1000000-1-111110000
χ222222222-2-22222222-2-2-2-2-22-12-1-1-1221111-1-1-1-1-2-2-1-11122-2-2-1-1-1-111111111-2-2-2-2000000220000001100000011-1-1-1-10000
χ232222222-2-22222222-2-2-2-2-2-12-1222-1-1-2-2-2-2-1-1-1-11122-2-2-1-111-1-1-1-11111111100000000000022-2-20000000000000000-1-111
χ242222222-2-22222222-2-2-2-2-2-12-1222-1-1-2-2-2-2-1-1-1-11122-2-2-1-111-1-1-1-111111111000000000000-2-222000000000000000011-1-1
χ2522222-2-222222-2-2-2-2-222-2-22-12-1-1-122-1-1-1-1-1-1-1-1-2-21111-2-2221111-1-1-1-1111122-2-20000002-2000000-1-100000011-1-1110000
χ2622222-2-222222-2-2-2-2-222-2-22-12-1-1-122-1-1-1-1-1-1-1-1-2-21111-2-2221111-1-1-1-11111-2-222000000-2200000011000000-1-111-1-10000
χ2722222-2-222222-2-2-2-2-222-2-2-12-1222-1-12222-1-1-1-111-2-2-2-211-1-11111-1-1-1-111110000000000002-22-20000000000000000-11-11
χ2822222-2-222222-2-2-2-2-222-2-2-12-1222-1-12222-1-1-1-111-2-2-2-211-1-11111-1-1-1-11111000000000000-22-2200000000000000001-11-1
χ2922222-2-2-2-2222-2-2-2-22-2-2222-12-1-1-1221111-1-1-1-12211-1-1-2-2-2-211111111-1-1-1-122-2-2000000-22000000-1-10000001111-1-10000
χ3022222-2-2-2-2222-2-2-2-22-2-2222-12-1-1-1221111-1-1-1-12211-1-1-2-2-2-211111111-1-1-1-1-2-2220000002-200000011000000-1-1-1-1110000
χ3122222-2-2-2-2222-2-2-2-22-2-222-12-1222-1-1-2-2-2-2-1-1-1-1-1-1-2-222111111111111-1-1-1-10000000000002-2-220000000000000000-111-1
χ3222222-2-2-2-2222-2-2-2-22-2-222-12-1222-1-1-2-2-2-2-1-1-1-1-1-1-2-222111111111111-1-1-1-1000000000000-222-200000000000000001-1-11
χ332-22-22002i−2i2-2-2000002i−2i0022-22-2-22-22i2i−2i−2i22-2-2000000002i−2i00002i2i−2i−2i000000002-22i−2i0000000000002-22i−2i000000000000
χ342-22-22002i−2i2-2-2000002i−2i0022-22-2-22-22i2i−2i−2i22-2-2000000002i−2i00002i2i−2i−2i00000000-22−2i2i000000000000-22−2i2i000000000000
χ352-22-2200−2i2i2-2-200000−2i2i0022-22-2-22-2−2i−2i2i2i22-2-200000000−2i2i0000−2i−2i2i2i000000002-2−2i2i0000000000002-2−2i2i000000000000
χ362-22-2200−2i2i2-2-200000−2i2i0022-22-2-22-2−2i−2i2i2i22-2-200000000−2i2i0000−2i−2i2i2i00000000-222i−2i000000000000-222i−2i000000000000
χ372-2-2222i−2i00-22-22i2i−2i−2i0000022-2-22-2-2200002-22-2002i−2i002i−2i002i2i−2i−2i000000002-22i−2i000000000000002-20000002i−2i00000000
χ382-2-2222i−2i00-22-22i2i−2i−2i0000022-2-22-2-2200002-22-2002i−2i002i−2i002i2i−2i−2i00000000-22−2i2i00000000000000-22000000−2i2i00000000
χ392-2-2222i−2i00-22-22i2i−2i−2i000002-1-21-11-22−i3i3−i3i3-11-1100−ii3−32i−2i00−i−iii−i3i3−i3i333−3−32-22i−2i00000000000000-11000000−ii−i3i33−30000
χ402-2-2222i−2i00-22-22i2i−2i−2i000002-1-21-11-22−i3i3−i3i3-11-1100−ii3−32i−2i00−i−iii−i3i3−i3i333−3−3-22−2i2i000000000000001-1000000i−ii3−i3−330000
χ412-2-2222i−2i00-22-22i2i−2i−2i000002-1-21-11-22i3−i3i3−i3-11-1100−ii−332i−2i00−i−iiii3−i3i3−i3−3−3332-22i−2i00000000000000-11000000−iii3−i3−330000
χ422-2-2222i−2i00-22-22i2i−2i−2i000002-1-21-11-22i3−i3i3−i3-11-1100−ii−332i−2i00−i−iiii3−i3i3−i3−3−333-22−2i2i000000000000001-1000000i−i−i3i33−30000
χ432-2-222−2i2i00-22-2−2i−2i2i2i0000022-2-22-2-2200002-22-200−2i2i00−2i2i00−2i−2i2i2i000000002-2−2i2i000000000000002-2000000−2i2i00000000
χ442-2-222−2i2i00-22-2−2i−2i2i2i0000022-2-22-2-2200002-22-200−2i2i00−2i2i00−2i−2i2i2i00000000-222i−2i00000000000000-220000002i−2i00000000
χ452-2-222−2i2i00-22-2−2i−2i2i2i000002-1-21-11-22−i3i3−i3i3-11-1100i−i−33−2i2i00ii−i−i−i3i3−i3i3−3−3332-2−2i2i00000000000000-11000000i−i−i3i3−330000
χ462-2-222−2i2i00-22-2−2i−2i2i2i000002-1-21-11-22−i3i3−i3i3-11-1100i−i−33−2i2i00ii−i−i−i3i3−i3i3−3−333-222i−2i000000000000001-1000000−iii3−i33−30000
χ472-2-222−2i2i00-22-2−2i−2i2i2i000002-1-21-11-22i3−i3i3−i3-11-1100i−i3−3−2i2i00ii−i−ii3−i3i3−i333−3−32-2−2i2i00000000000000-11000000i−ii3−i33−30000
χ482-2-222−2i2i00-22-2−2i−2i2i2i000002-1-21-11-22i3−i3i3−i3-11-1100i−i3−3−2i2i00ii−i−ii3−i3i3−i333−3−3-222i−2i000000000000001-1000000−ii−i3i3−330000
χ49444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000
χ504444444-4-44444444-4-4-4-4-4-2-2-2-2-2-2-2-22222111122-2-222-2-2221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5144444-4-444444-4-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-2111122222222-2-2-1-1-1-11111-1-1-1-1000000000000000000000000000000000000
χ5244444-4-4-4-4444-4-4-4-44-4-444-2-2-2-2-2-2-2-222221111-2-222-2-22222-1-1-1-1-1-1-1-11111000000000000000000000000000000000000
χ5344-4-440000-4-44000000000444-4-44-4-400004-4-440000000000000000000000000000000000000000000000000000000000
χ5444-4-440000-4-440000000004-2422-2-4-423−23−2323-222-20000000000000023−23−23230000000000000000000000000000000000000000
χ5544-4-440000-4-440000000004-2422-2-4-4−232323−23-222-200000000000000−232323−230000000000000000000000000000000000000000
χ5644-4-440000-4-44000000000-24-2-4-44220000-222-2−2i32i30000000000000000−2i32i3−2i32i3000000000000000000000000000000000000
χ5744-4-440000-4-44000000000-24-2-4-44220000-222-22i3−2i300000000000000002i3−2i32i3−2i3000000000000000000000000000000000000
χ5844-4-440000-4-44000000000-2-2-222-22223−23−23231-1-11−2i32i3000000003i−3i3i−3i−333−3i3−i3i3−i3000000000000000000000000000000000000
χ5944-4-440000-4-44000000000-2-2-222-22223−23−23231-1-112i3−2i300000000−3i3i−3i3i−333−3−i3i3−i3i3000000000000000000000000000000000000
χ6044-4-440000-4-44000000000-2-2-222-222−232323−231-1-11−2i32i300000000−3i3i−3i3i3−3−33i3−i3i3−i3000000000000000000000000000000000000
χ6144-4-440000-4-44000000000-2-2-222-222−232323−231-1-112i3−2i3000000003i−3i3i−3i3−3−33−i3i3−i3i3000000000000000000000000000000000000
χ624-44-44004i−4i4-4-4000004i−4i004-2-4-2224-4−2i−2i2i2i-2-222000000004i−4i0000−2i−2i2i2i0000000000000000000000000000000000000000
χ634-44-44004i−4i4-4-4000004i−4i00-2424-4-4-224i4i−4i−4i-2-22200000000−2i2i0000−2i−2i2i2i0000000000000000000000000000000000000000
χ644-44-44004i−4i4-4-4000004i−4i00-2-22-222-22−2i−2i2i2i11-1-100000000−2i2i3-3-33ii−i−i3i−3i−3i3i000000000000000000000000000000000000
χ654-44-44004i−4i4-4-4000004i−4i00-2-22-222-22−2i−2i2i2i11-1-100000000−2i2i-333-3ii−i−i−3i3i3i−3i000000000000000000000000000000000000
χ664-44-4400−4i4i4-4-400000−4i4i004-2-4-2224-42i2i−2i−2i-2-22200000000−4i4i00002i2i−2i−2i0000000000000000000000000000000000000000
χ674-44-4400−4i4i4-4-400000−4i4i00-2424-4-4-22−4i−4i4i4i-2-222000000002i−2i00002i2i−2i−2i0000000000000000000000000000000000000000
χ684-44-4400−4i4i4-4-400000−4i4i00-2-22-222-222i2i−2i−2i11-1-1000000002i−2i3-3-33−i−iii−3i3i3i−3i000000000000000000000000000000000000
χ694-44-4400−4i4i4-4-400000−4i4i00-2-22-222-222i2i−2i−2i11-1-1000000002i−2i-333-3−i−iii3i−3i−3i3i000000000000000000000000000000000000
χ704-4-4444i−4i00-44-44i4i−4i−4i00000-242-44-42-20000-22-22004i−4i00−2i2i00−2i−2i2i2i00000000000000000000000000000000000000000000
χ714-4-4444i−4i00-44-44i4i−4i−4i00000-2-222-222-2−2i32i3−2i32i31-11-100−2i2i23−23−2i2i00ii−i−ii3−i3i3−i3−3−333000000000000000000000000000000000000
χ724-4-4444i−4i00-44-44i4i−4i−4i00000-2-222-222-22i3−2i32i3−2i31-11-100−2i2i−2323−2i2i00ii−i−i−i3i3−i3i333−3−3000000000000000000000000000000000000
χ734-4-444−4i4i00-44-4−4i−4i4i4i00000-242-44-42-20000-22-2200−4i4i002i−2i002i2i−2i−2i00000000000000000000000000000000000000000000
χ744-4-444−4i4i00-44-4−4i−4i4i4i00000-2-222-222-2−2i32i3−2i32i31-11-1002i−2i−23232i−2i00−i−iiii3−i3i3−i333−3−3000000000000000000000000000000000000
χ754-4-444−4i4i00-44-4−4i−4i4i4i00000-2-222-222-22i3−2i32i3−2i31-11-1002i−2i23−232i−2i00−i−iii−i3i3−i3i3−3−333000000000000000000000000000000000000
χ766666-36666-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000222222000000-1-100-1-1-1-1-1-10000000000
χ776666-36666-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000-2-2-2-2-2-200000011001111110000000000
χ786666-366-6-6-3-3-3-3-3-3-3-6333300000000000000000000000000000000000000000022-2-22-2000000-1-100-1-111110000000000
χ796666-366-6-6-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000-2-222-22000000110011-1-1-1-10000000000
χ806666-3-6-666-3-3-33333-6-3-3330000000000000000000000000000000000000000002222-2-20000001100-1-1-1-1110000000000
χ816666-3-6-666-3-3-33333-6-3-333000000000000000000000000000000000000000000-2-2-2-222000000-1-1001111-1-10000000000
χ826666-3-6-6-6-6-3-3-33333633-3-300000000000000000000000000000000000000000022-2-2-220000001100-1-111-1-10000000000
χ836666-3-6-6-6-6-3-3-33333633-3-3000000000000000000000000000000000000000000-2-2222-2000000-1-10011-1-1110000000000
χ846-66-6-3006i−6i-333−3i33i3−3i33i30−3i3i33−330000000000000000000000000000000000000000002-22i−2i00000000−i3i300-11−ii3−30000000000
χ856-66-6-3006i−6i-333−3i33i3−3i33i30−3i3i33−33000000000000000000000000000000000000000000-22−2i2i00000000i3−i3001-1i−i−330000000000
χ866-66-6-3006i−6i-3333i3−3i33i3−3i30−3i3i−33330000000000000000000000000000000000000000002-22i−2i00000000i3−i300-11−ii−330000000000
χ876-66-6-3006i−6i-3333i3−3i33i3−3i30−3i3i−3333000000000000000000000000000000000000000000-22−2i2i00000000−i3i3001-1i−i3−30000000000
χ886-66-6-300−6i6i-333−3i33i3−3i33i303i−3i−33330000000000000000000000000000000000000000002-2−2i2i00000000−i3i300-11i−i−330000000000
χ896-66-6-300−6i6i-333−3i33i3−3i33i303i−3i−3333000000000000000000000000000000000000000000-222i−2i00000000i3−i3001-1−ii3−30000000000
χ906-66-6-300−6i6i-3333i3−3i33i3−3i303i−3i33−330000000000000000000000000000000000000000002-2−2i2i00000000i3−i300-11i−i3−30000000000
χ916-66-6-300−6i6i-3333i3−3i33i3−3i303i−3i33−33000000000000000000000000000000000000000000-222i−2i00000000−i3i3001-1−ii−330000000000
χ921212-12-12-6000066-663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000000000
χ931212-12-12-6000066-6−636363−630000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-1212-612i−12i006-66−6i−6i6i6i0000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-6−12i12i006-666i6i−6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000000

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