Finite Group Databasebeta

← Group #13167585

Character table — Group #13167585

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222224444444444444488888888888888888899991818181818181818181818181818363636363636363636363636363636363636363636363636363672727272
order122222366633666666666666336666666666666666222222444444446666224444446612121212121212121212121212121212661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111-1-1111111-1-111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111-1-1111111-1-111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111-1-1111111-1-111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ81111-1-1111111-1-111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ91-11-11-111-1-1111-11-111-1-1-1-11-1111-111-1-1-1-11111-1-1-1-111-1-11-1ii−i−iii−i−i11-1-11-11-1i−ii−i1-1ii−i−iii−i−iii−i−iii−i−i1-11-1
χ101-11-11-111-1-1111-11-111-1-1-1-11-1111-111-1-1-1-11111-1-1-1-111-1-11-1ii−i−iii−i−i11-1-1-11-11−ii−ii1-1ii−i−iii−i−i−i−iii−i−iii-11-11
χ111-11-11-111-1-1111-11-111-1-1-1-11-1111-111-1-1-1-11111-1-1-1-111-1-11-1−i−iii−i−iii11-1-11-11-1−ii−ii1-1−i−iii−i−iii−i−iii−i−iii1-11-1
χ121-11-11-111-1-1111-11-111-1-1-1-11-1111-111-1-1-1-11111-1-1-1-111-1-11-1−i−iii−i−iii11-1-1-11-11i−ii−i1-1−i−iii−i−iiiii−i−iii−i−i-11-11
χ131-11-1-1111-1-111-111-1-1-111-1-11-111-1111-1-1-1-1-1-1-1-1111111-1-1-11ii−i−i−i−iii11-1-11-1-11i−i−ii-11ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ141-11-1-1111-1-111-111-1-1-111-1-11-111-1111-1-1-1-1-1-1-1-1111111-1-1-11ii−i−i−i−iii11-1-1-111-1−iii−i-11ii−i−i−i−iii−i−iiiii−i−i-111-1
χ151-11-1-1111-1-111-111-1-1-111-1-11-111-1111-1-1-1-1-1-1-1-1111111-1-1-11−i−iiiii−i−i11-1-11-1-11−iii−i-11−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ161-11-1-1111-1-111-111-1-1-111-1-11-111-1111-1-1-1-1-1-1-1-1111111-1-1-11−i−iiiii−i−i11-1-1-111-1i−i−ii-11−i−iiiii−i−iii−i−i−i−iii-111-1
χ17222222222222222222222222222222222222222222-2-2-2-2-2-200000000-2-2-2-200000000-2-200000000000000000000
χ18222222-1-1-1-122-1-12222222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-122222200000000-1-1-1-100002222-1-100000000-1-1-1-1-1-1-1-10000
χ19222222-1-1-1-122-1-12222222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-122222200000000-1-1-1-10000-2-2-2-2-1-100000000111111110000
χ20222222-1-1-1-122-1-12222222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-20000000011110000000011000000003−33−33−33−30000
χ21222222-1-1-1-122-1-12222222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2000000001111000000001100000000−33−33−33−330000
χ222222-2-2222222-2-222-2-2-2-2222222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-22200000000-2-2-2-2000000002200000000000000000000
χ232222-2-2-1-1-1-1221122-2-2-2-22222-1-1-2-2-1-1-1-1-1-1111111112222-2-200000000-1-1-1-1000022-2-21100000000-1-1-1-111110000
χ242222-2-2-1-1-1-1221122-2-2-2-22222-1-1-2-2-1-1-1-1-1-1111111112222-2-200000000-1-1-1-10000-2-22211000000001111-1-1-1-10000
χ252222-2-2-1-1-1-1221122-2-2-2-22222-1-1-2-2-1-1-1-1-1-111111111-2-2-2-22200000000111100000000-1-1000000003−33−3−33−330000
χ262222-2-2-1-1-1-1221122-2-2-2-22222-1-1-2-2-1-1-1-1-1-111111111-2-2-2-22200000000111100000000-1-100000000−33−333−33−30000
χ2722-2-2002-22-22200-2200002-2-2-22200-2-222-2-2000000002-22-20000002i−2i2i−2i2-22-2000000000000002i−2i2i−2i000000000000
χ2822-2-2002-22-22200-2200002-2-2-22200-2-222-2-2000000002-22-2000000−2i2i−2i2i2-22-200000000000000−2i2i−2i2i000000000000
χ2922-2-2002-22-22200-2200002-2-2-22200-2-222-2-200000000-22-22002i−2i2i−2i0000-22-2200000000002i−2i2i−2i0000000000000000
χ3022-2-2002-22-22200-2200002-2-2-22200-2-222-2-200000000-22-2200−2i2i−2i2i0000-22-220000000000−2i2i−2i2i0000000000000000
χ312-22-22-222-2-2222-22-222-2-2-2-22-2222-222-2-2-2-22222-2-2-2-2-2-222-2200000000-2-22200000000-2200000000000000000000
χ322-22-22-2-1-11122-112-222-2-2-2-22-2-1-12-2-1-11111-1-1-1-1111122-2-22-200000000-1-11100002i−2i2i−2i-1100000000−i−iii−i−iii0000
χ332-22-22-2-1-11122-112-222-2-2-2-22-2-1-12-2-1-11111-1-1-1-1111122-2-22-200000000-1-1110000−2i2i−2i2i-1100000000ii−i−iii−i−i0000
χ342-22-22-2-1-11122-112-222-2-2-2-22-2-1-12-2-1-11111-1-1-1-11111-2-222-220000000011-1-1000000001-100000000−i3i3i3−i3−i3i3i3−i30000
χ352-22-22-2-1-11122-112-222-2-2-2-22-2-1-12-2-1-11111-1-1-1-11111-2-222-220000000011-1-1000000001-100000000i3−i3−i3i3i3−i3−i3i30000
χ362-22-2-2222-2-222-222-2-2-222-2-22-222-2222-2-2-2-2-2-2-2-22222-2-2222-200000000-2-222000000002-200000000000000000000
χ372-22-2-22-1-111221-12-2-2-222-2-22-2-1-1-22-1-111111111-1-1-1-122-2-2-2200000000-1-11100002i−2i−2i2i1-100000000−i−iiiii−i−i0000
χ382-22-2-22-1-111221-12-2-2-222-2-22-2-1-1-22-1-111111111-1-1-1-122-2-2-2200000000-1-1110000−2i2i2i−2i1-100000000ii−i−i−i−iii0000
χ392-22-2-22-1-111221-12-2-2-222-2-22-2-1-1-22-1-111111111-1-1-1-1-2-2222-20000000011-1-100000000-1100000000−i3i3i3−i3i3−i3−i3i30000
χ402-22-2-22-1-111221-12-2-2-222-2-22-2-1-1-22-1-111111111-1-1-1-1-2-2222-20000000011-1-100000000-1100000000i3−i3−i3i3−i3i3i3−i30000
χ412-2-22002-2-222200-2-20000-22-222200-2-2-2-222000000002-2-220000002-2-222-2-22000000000000002-2-22000000000000
χ422-2-22002-2-222200-2-20000-22-222200-2-2-2-222000000002-2-22000000-222-22-2-2200000000000000-222-2000000000000
χ432-2-22002-2-222200-2-20000-22-222200-2-2-2-22200000000-222-2002-2-220000-222-200000000002-2-220000000000000000
χ442-2-22002-2-222200-2-20000-22-222200-2-2-2-22200000000-222-200-222-20000-222-20000000000-222-20000000000000000
χ4544444444441-244111111-2-2-211-2-2-21-21-21-211-2-211-2-20000002222222200000000000000-1-1-1-1-1-1-1-1000000000000
χ4644444444441-244111111-2-2-211-2-2-21-21-21-211-2-211-2-2000000-2-2-2-2-2-2-2-20000000000000011111111000000000000
χ474444444444-2144-2-2-2-2-2-2111-2-2111-21-21-21-2-211-2-21100000000000000000022220000000000000000000000-1-1-1-1
χ484444444444-2144-2-2-2-2-2-2111-2-2111-21-21-21-2-211-2-211000000000000000000-2-2-2-200000000000000000000001111
χ494444-4-444441-2-4-411-1-1-1-1-2-2-211-2221-21-21-2-1-122-1-1220000002222-2-2-2-200000000000000-1-1-1-11111000000000000
χ504444-4-444441-2-4-411-1-1-1-1-2-2-211-2221-21-21-2-1-122-1-122000000-2-2-2-22222000000000000001111-1-1-1-1000000000000
χ514444-4-44444-21-4-4-2-22222111-2-21-1-1-21-21-2122-1-122-1-100000000000000000022-2-20000000000000000000000-1-111
χ524444-4-44444-21-4-4-2-22222111-2-21-1-1-21-21-2122-1-122-1-1000000000000000000-2-222000000000000000000000011-1-1
χ5344-4-4004-44-41-200-113-33-3-222-11-200-121-2-123-3003-3000000002i−2i2i−2i2i−2i2i−2i00000000000000−ii−ii−ii−ii000000000000
χ5444-4-4004-44-41-200-113-33-3-222-11-200-121-2-123-3003-300000000−2i2i−2i2i−2i2i−2i2i00000000000000i−ii−ii−ii−i000000000000
χ5544-4-4004-44-41-200-11-33-33-222-11-200-121-2-12-3300-33000000002i−2i2i−2i−2i2i−2i2i00000000000000−ii−iii−ii−i000000000000
χ5644-4-4004-44-41-200-11-33-33-222-11-200-121-2-12-3300-3300000000−2i2i−2i2i2i−2i2i−2i00000000000000i−ii−i−ii−ii000000000000
χ5744-4-400-22-224400-4400004-4-4-4-2-20022-2-222000000004-44-40000000000-22-22000000000000000000000000000000
χ5844-4-400-22-224400-4400004-4-4-4-2-20022-2-22200000000-44-4400000000002-22-2000000000000000000000000000000
χ594-44-44-444-4-41-24-41-111-1-122-2-11-2-221-2-12-1211-2-2-1-1220000002i2i−2i−2i2i2i−2i−2i00000000000000−i−iii−i−iii000000000000
χ604-44-44-444-4-41-24-41-111-1-122-2-11-2-221-2-12-1211-2-2-1-122000000−2i−2i2i2i−2i−2i2i2i00000000000000ii−i−iii−i−i000000000000
χ614-44-44-444-4-4-214-4-22-2-222-1-112-211-1-212-12-1-2-21122-1-10000000000000000002-22-20000000000000000000000-11-11
χ624-44-44-444-4-4-214-4-22-2-222-1-112-211-1-212-12-1-2-21122-1-1000000000000000000-22-2200000000000000000000001-11-1
χ634-44-4-4444-4-41-2-441-1-1-11122-2-11-22-21-2-12-12-1-12211-2-20000002i2i−2i−2i−2i−2i2i2i00000000000000−i−iiiii−i−i000000000000
χ644-44-4-4444-4-41-2-441-1-1-11122-2-11-22-21-2-12-12-1-12211-2-2000000−2i−2i2i2i2i2i−2i−2i00000000000000ii−i−i−i−iii000000000000
χ654-44-4-4444-4-4-21-44-2222-2-2-1-112-21-11-212-12-122-1-1-2-2110000000000000000002-2-220000000000000000000000-111-1
χ664-44-4-4444-4-4-21-44-2222-2-2-1-112-21-11-212-12-122-1-1-2-211000000000000000000-222-200000000000000000000001-1-11
χ674-4-44004-4-441-200-1-13-3-332-2211-200-12-121-23-300-33000000002-2-222-2-2200000000000000-111-1-111-1000000000000
χ684-4-44004-4-441-200-1-13-3-332-2211-200-12-121-23-300-3300000000-222-2-222-2000000000000001-1-111-1-11000000000000
χ694-4-44004-4-441-200-1-1-333-32-2211-200-12-121-2-33003-3000000002-2-22-222-200000000000000-111-11-1-11000000000000
χ704-4-44004-4-441-200-1-1-333-32-2211-200-12-121-2-33003-300000000-222-22-2-22000000000000001-1-11-111-1000000000000
χ714-4-4400-222-24400-4-40000-44-44-2-2002222-2-2000000004-4-440000000000-222-2000000000000000000000000000000
χ724-4-4400-222-24400-4-40000-44-44-2-2002222-2-200000000-444-400000000002-2-22000000000000000000000000000000
χ73888888-4-4-4-42-4-4-4222222-4-4-42-12-4-4-12-12-12-1-122-1-122000000000000000000000000000000000000000000000000
χ74888888-4-4-4-4-42-4-4-4-4-4-4-4-4222-42-1222-12-12-122-1-122-1-1000000000000000000000000000000000000000000000000
χ758888-8-8-4-4-4-42-44422-2-2-2-2-4-4-42-1244-12-12-1211-2-211-2-2000000000000000000000000000000000000000000000000
χ768888-8-8-4-4-4-4-4244-4-44444222-42-1-2-22-12-12-1-2-211-2-211000000000000000000000000000000000000000000000000
χ7788-8-8008-88-8-42004-400002-2-24-42004-2-424-200000000000000000000000000000000000000000000000000000000
χ7888-8-800-44-442-400-226-66-6-444-2-12001-2-121-2-3300-3300000000000000000000000000000000000000000000000000
χ7988-8-800-44-442-400-22-66-66-444-2-12001-2-121-23-3003-300000000000000000000000000000000000000000000000000
χ8088-8-800-44-44-42004-400002-2-242-100-212-1-2100−3i33i300−3i33i3000000000000000000000000000000000000000000000000
χ8188-8-800-44-44-42004-400002-2-242-100-212-1-21003i3−3i3003i3−3i3000000000000000000000000000000000000000000000000
χ828-88-88-8-4-4442-4-442-222-2-244-4-2-12-44-121-21-2-1-12211-2-2000000000000000000000000000000000000000000000000
χ838-88-88-8-4-444-42-44-44-4-444-2-2242-12-22-1-21-2122-1-1-2-211000000000000000000000000000000000000000000000000
χ848-88-8-88-4-4442-44-42-2-2-22244-4-2-124-4-121-21-211-2-2-1-122000000000000000000000000000000000000000000000000
χ858-88-8-88-4-444-424-4-4444-4-4-2-2242-1-222-1-21-21-2-21122-1-1000000000000000000000000000000000000000000000000
χ868-8-88008-8-88-4200440000-22-2-4-42004-24-2-4200000000000000000000000000000000000000000000000000000000
χ878-8-8800-444-42-400-2-26-6-664-442-12001-21-2-12-33003-300000000000000000000000000000000000000000000000000
χ888-8-8800-444-42-400-2-2-666-64-442-12001-21-2-123-300-3300000000000000000000000000000000000000000000000000
χ898-8-8800-444-4-4200440000-22-2-42-100-21-212-100−3i33i3003i3−3i3000000000000000000000000000000000000000000000000
χ908-8-8800-444-4-4200440000-22-2-42-100-21-212-1003i3−3i300−3i33i3000000000000000000000000000000000000000000000000

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