Finite Group Databasebeta

← Group #13167529

Character table — Group #13167529

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222224444444444444488888888888888888899991818181818181818181818181818363636363636363636363636363636363636363636363636363672727272
order12223446663366666612121212121233666666121212121212121212122222222244444466662244444466661212121212121212121212121212661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ511111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ811111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ911-1-11i−i1-1-11111-1-1-1-1i−iii−i−i1111-1-1-1-1i−iiiii−i−i−i−i1-11-111-1-1i−iii−i−i1-11-11-1i−i1-1i−i11-1-1i−iii−i−i11-1-1ii−i−i1-1i−i
χ1011-1-11i−i1-1-11111-1-1-1-1i−iii−i−i1111-1-1-1-1i−iiiii−i−i−i−i1-11-111-1-1i−iii−i−i1-11-1-11−ii-11−ii11-1-1i−iii−i−i-1-111−i−iii-11−ii
χ1111-1-11i−i1-1-11111-1-1-1-1i−iii−i−i1111-1-1-1-1i−iiiii−i−i−i−i1-11-1-1-111i−i−i−iii1-11-11-1i−i-11−ii-1-111i−i−i−iii-1-111−i−iii1-1i−i
χ1211-1-11i−i1-1-11111-1-1-1-1i−iii−i−i1111-1-1-1-1i−iiiii−i−i−i−i1-11-1-1-111i−i−i−iii1-11-1-11−ii1-1i−i-1-111i−i−i−iii11-1-1ii−i−i-11−ii
χ1311-1-11−ii1-1-11111-1-1-1-1−ii−i−iii1111-1-1-1-1−ii−i−i−i−iiiii1-11-111-1-1−ii−i−iii1-11-11-1−ii1-1−ii11-1-1−ii−i−iii11-1-1−i−iii1-1−ii
χ1411-1-11−ii1-1-11111-1-1-1-1−ii−i−iii1111-1-1-1-1−ii−i−i−i−iiiii1-11-111-1-1−ii−i−iii1-11-1-11i−i-11i−i11-1-1−ii−i−iii-1-111ii−i−i-11i−i
χ1511-1-11−ii1-1-11111-1-1-1-1−ii−i−iii1111-1-1-1-1−ii−i−i−i−iiiii1-11-1-1-111−iiii−i−i1-11-11-1−ii-11i−i-1-111−iiii−i−i-1-111ii−i−i1-1−ii
χ1611-1-11−ii1-1-11111-1-1-1-1−ii−i−iii1111-1-1-1-1−ii−i−i−i−iiiii1-11-1-1-111−iiii−i−i1-11-1-11i−i1-1−ii-1-111−iiii−i−i11-1-1−i−iii-11i−i
χ17222222222222222222222222222222222222222222-2-2-2-20000-2-20000-2-2-2-2000000000000-2-20000000000000000
χ1822222-2-222222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000220000-2-2-2-2000000000000220000000000000000
χ192222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122220000220000-1-1-1-1000022220000-1-10000-1-1-1-1-1-1-1-10000
χ202222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122220000220000-1-1-1-10000-2-2-2-20000-1-10000111111110000
χ212222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-20000-2-2000011110000000000001100003−33−33−33−30000
χ222222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-20000-2-200001111000000000000110000−33−33−33−330000
χ232222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-21111111122220000-2-20000-1-1-1-1000022-2-20000110000-1-1-1-111110000
χ242222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-21111111122220000-2-20000-1-1-1-10000-2-22200001100001111-1-1-1-10000
χ252222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-2-2-200002200001111000000000000-1-100003−33−3−33−330000
χ262222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-2-2-200002200001111000000000000-1-10000−33−333−33−30000
χ2722-2-222i−2i2-2-22222-2-2-2-22i−2i2i2i−2i−2i2222-2-2-2-22i−2i2i2i2i2i−2i−2i−2i−2i-22-220000−2i2i0000-22-22000000000000−2i2i0000000000000000
χ2822-2-22−2i2i2-2-22222-2-2-2-2−2i2i−2i−2i2i2i2222-2-2-2-2−2i2i−2i−2i−2i−2i2i2i2i2i-22-2200002i−2i0000-22-220000000000002i−2i0000000000000000
χ2922-2-2-12i−2i-1112222-2-2-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii2-22-200002i−2i0000-11-1100002-22i−2i0000−ii0000-1-111−i−iii0000
χ3022-2-2-12i−2i-1112222-2-2-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii2-22-200002i−2i0000-11-110000-22−2i2i0000−ii000011-1-1ii−i−i0000
χ3122-2-2-12i−2i-1112222-2-2-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii-22-220000−2i2i00001-11-1000000000000i−i00003−3−33i3−i3−i3i30000
χ3222-2-2-12i−2i-1112222-2-2-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii-22-220000−2i2i00001-11-1000000000000i−i0000−333−3−i3i3i3−i30000
χ3322-2-2-1−2i2i-1112222-2-2-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i2-22-20000−2i2i0000-11-1100002-2−2i2i0000i−i0000-1-111ii−i−i0000
χ3422-2-2-1−2i2i-1112222-2-2-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i2-22-20000−2i2i0000-11-110000-222i−2i0000i−i000011-1-1−i−iii0000
χ3522-2-2-1−2i2i-1112222-2-2-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i-22-2200002i−2i00001-11-1000000000000−ii00003−3−33−i3i3i3−i30000
χ3622-2-2-1−2i2i-1112222-2-2-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i-22-2200002i−2i00001-11-1000000000000−ii0000−333−3i3−i3−i3i30000
χ372-22-2200-22-222-2-22-22-200000022-2-222-2-2000000000022-2-20000002i−2i2i−2i22-2-2000000000000002i−2i2i−2i000000000000
χ382-22-2200-22-222-2-22-22-200000022-2-222-2-2000000000022-2-2000000−2i2i−2i2i22-2-200000000000000−2i2i−2i2i000000000000
χ392-22-2200-22-222-2-22-22-200000022-2-222-2-20000000000-2-2222-22-2000000-2-222000000002-22-2000000000000000000
χ402-22-2200-22-222-2-22-22-200000022-2-222-2-20000000000-2-222-22-22000000-2-22200000000-22-22000000000000000000
χ412-2-22200-2-2222-2-2-22-2200000022-2-2-2-22200000000002-2-220000002-2-222-2-22000000000000002-2-22000000000000
χ422-2-22200-2-2222-2-2-22-2200000022-2-2-2-22200000000002-2-22000000-222-22-2-2200000000000000-222-2000000000000
χ432-2-22200-2-2222-2-2-22-2200000022-2-2-2-2220000000000-222-22-2-22000000-222-2000000002-2-22000000000000000000
χ442-2-22200-2-2222-2-2-22-2200000022-2-2-2-2220000000000-222-2-222-2000000-222-200000000-222-2000000000000000000
χ4544444444441-21-21-2-214411111-21-21-21-2-2-211-2-211-2-200002222002222000000000000-1-1-1-100-1-1-1-1000000000000
χ4644444444441-21-21-2-214411111-21-21-21-2-2-211-2-211-2-20000-2-2-2-200-2-2-2-20000000000001111001111000000000000
χ474444444444-21-21-211-244-2-2-2-2-21-21-21-2111-2-211-2-21100000000000000000022220000000000000000000000-1-1-1-1
χ484444444444-21-21-211-244-2-2-2-2-21-21-21-2111-2-211-2-211000000000000000000-2-2-2-200000000000000000000001111
χ4944444-4-44441-21-21-2-21-4-4-1-1-1-11-21-21-21-222-1-122-1-1220000222200-2-2-2-2000000000000-1-1-1-1001111000000000000
χ5044444-4-44441-21-21-2-21-4-4-1-1-1-11-21-21-21-222-1-122-1-1220000-2-2-2-2002222000000000000111100-1-1-1-1000000000000
χ5144444-4-4444-21-21-211-2-4-42222-21-21-21-21-1-122-1-122-1-100000000000000000022-2-20000000000000000000000-1-111
χ5244444-4-4444-21-21-211-2-4-42222-21-21-21-21-1-122-1-122-1-1000000000000000000-2-222000000000000000000000011-1-1
χ5344-4-444i−4i4-4-41-21-2-122-14i−4iii−i−i1-21-2-12-12−2i2iii−2i−2i−i−i2i2i000022-2-2002i2i−2i−2i000000000000-1-11100−i−iii000000000000
χ5444-4-444i−4i4-4-41-21-2-122-14i−4iii−i−i1-21-2-12-12−2i2iii−2i−2i−i−i2i2i0000-2-22200−2i−2i2i2i00000000000011-1-100ii−i−i000000000000
χ5544-4-444i−4i4-4-4-21-212-1-124i−4i−2i−2i2i2i-21-212-12-1i−i−2i−2iii2i2i−i−i0000000000000000002-22i−2i0000000000000000000000-11−ii
χ5644-4-444i−4i4-4-4-21-212-1-124i−4i−2i−2i2i2i-21-212-12-1i−i−2i−2iii2i2i−i−i000000000000000000-22−2i2i00000000000000000000001-1i−i
χ5744-4-44−4i4i4-4-41-21-2-122-1−4i4i−i−iii1-21-2-12-122i−2i−i−i2i2iii−2i−2i000022-2-200−2i−2i2i2i000000000000-1-11100ii−i−i000000000000
χ5844-4-44−4i4i4-4-41-21-2-122-1−4i4i−i−iii1-21-2-12-122i−2i−i−i2i2iii−2i−2i0000-2-222002i2i−2i−2i00000000000011-1-100−i−iii000000000000
χ5944-4-44−4i4i4-4-4-21-212-1-12−4i4i2i2i−2i−2i-21-212-12-1−ii2i2i−i−i−2i−2iii0000000000000000002-2−2i2i0000000000000000000000-11i−i
χ6044-4-44−4i4i4-4-4-21-212-1-12−4i4i2i2i−2i−2i-21-212-12-1−ii2i2i−i−i−2i−2iii000000000000000000-222i−2i00000000000000000000001-1−ii
χ614-44-4400-44-41-2-1212-2-1003i−3i3i−3i1-2-121-2-12003i−3i003i−3i0000002-22-2002i−2i2i−2i000000000000-11-1100−ii−ii000000000000
χ624-44-4400-44-41-2-1212-2-1003i−3i3i−3i1-2-121-2-12003i−3i003i−3i000000-22-2200−2i2i−2i2i0000000000001-11-100i−ii−i000000000000
χ634-44-4400-44-41-2-1212-2-100−3i3i−3i3i1-2-121-2-1200−3i3i00−3i3i0000002-22-200−2i2i−2i2i000000000000-11-1100i−ii−i000000000000
χ644-44-4400-44-41-2-1212-2-100−3i3i−3i3i1-2-121-2-1200−3i3i00−3i3i000000-22-22002i−2i2i−2i0000000000001-11-100−ii−ii000000000000
χ654-44-4-2002-2244-4-44-44-4000000-2-222-2-222000000000044-4-40000000000-2-222000000000000000000000000000000
χ664-44-4-2002-2244-4-44-44-4000000-2-222-2-2220000000000-4-444000000000022-2-2000000000000000000000000000000
χ674-4-44400-4-441-2-12-1-221003-3-331-2-12-121-2003-300-330000002-2-22002-2-22000000000000-111-100-111-1000000000000
χ684-4-44400-4-441-2-12-1-221003-3-331-2-12-121-2003-300-33000000-222-200-222-20000000000001-1-11001-1-11000000000000
χ694-4-44400-4-441-2-12-1-22100-333-31-2-12-121-200-33003-30000002-2-2200-222-2000000000000-111-1001-1-11000000000000
χ704-4-44400-4-441-2-12-1-22100-333-31-2-12-121-200-33003-3000000-222-2002-2-220000000000001-1-1100-111-1000000000000
χ714-4-44-20022-244-4-4-44-44000000-2-22222-2-200000000004-4-440000000000-222-2000000000000000000000000000000
χ724-4-44-20022-244-4-4-44-44000000-2-22222-2-20000000000-444-400000000002-2-22000000000000000000000000000000
χ738888-488-4-4-42-42-42-4-42-4-42222-12-12-12-12-4-4-1-122-1-122000000000000000000000000000000000000000000000000
χ748888-488-4-4-4-42-42-422-4-4-4-4-4-4-42-12-12-12-12222-1-122-1-1000000000000000000000000000000000000000000000000
χ758888-4-8-8-4-4-42-42-42-4-4244-2-2-2-2-12-12-12-124411-2-211-2-2000000000000000000000000000000000000000000000000
χ768888-4-8-8-4-4-4-42-42-422-44444442-12-12-12-1-2-2-2-211-2-211000000000000000000000000000000000000000000000000
χ7788-8-8-48i−8i-4442-42-4-244-2−4i4i2i2i−2i−2i-12-121-21-2−4i4i−i−i2i2iii−2i−2i000000000000000000000000000000000000000000000000
χ7888-8-8-48i−8i-444-42-424-2-24−4i4i−4i−4i4i4i2-12-1-21-212i−2i2i2i−i−i−2i−2iii000000000000000000000000000000000000000000000000
χ7988-8-8-4−8i8i-4442-42-4-244-24i−4i−2i−2i2i2i-12-121-21-24i−4iii−2i−2i−i−i2i2i000000000000000000000000000000000000000000000000
χ8088-8-8-4−8i8i-444-42-424-2-244i−4i4i4i−4i−4i2-12-1-21-21−2i2i−2i−2iii2i2i−i−i000000000000000000000000000000000000000000000000
χ818-88-8800-88-8-424-2-4-224000000-424-2-424-20000000000000000000000000000000000000000000000000000000000
χ828-88-8-4004-442-4-2424-4-2006i−6i6i−6i-121-2-121-200−3i3i00−3i3i00000000000000000000000000000000000000000000000000
χ838-88-8-4004-442-4-2424-4-200−6i6i−6i6i-121-2-121-2003i−3i003i−3i00000000000000000000000000000000000000000000000000
χ848-88-8-4004-44-424-2-4-2240000002-1-212-1-21000033−330033−33000000000000000000000000000000000000000000000000
χ858-88-8-4004-44-424-2-4-2240000002-1-212-1-210000−333300−3333000000000000000000000000000000000000000000000000
χ868-8-88800-8-88-424-242-2-4000000-424-24-2-420000000000000000000000000000000000000000000000000000000000
χ878-8-88-40044-42-4-24-2-442006-6-66-121-21-2-1200-33003-300000000000000000000000000000000000000000000000000
χ888-8-88-40044-42-4-24-2-44200-666-6-121-21-2-12003-300-3300000000000000000000000000000000000000000000000000
χ898-8-88-40044-4-424-242-2-40000002-1-21-212-10000−3i33i3003i3−3i3000000000000000000000000000000000000000000000000
χ908-8-88-40044-4-424-242-2-40000002-1-21-212-100003i3−3i300−3i33i3000000000000000000000000000000000000000000000000

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