Finite Group Databasebeta

← Group #11774537

Character table — Group #11774537

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111444444444444444444888888881212121212121212181818181818181824242424242424242424242424242424242424243636363636363636
order1222444423346666661212121212121212666612121212888888884444444444441212121212121212242424242424242488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111-111-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111-111-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ711111111-111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ811111111-111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−i1111-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−i1111-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ111111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii1111-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ121111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii1111-1-1-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii11-1-111-1-11-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii11-1-111-1-1-111-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ151111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i11-1-111-1-11-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ161111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i11-1-111-1-1-111-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222-222-222222222222222-2-2-2-2-2-2-2-200000000-2-22222-2-20000000000000000000000000000
χ192222-2-2-2-2222-2222222-2-2-2-2-2-2-2-22222-2-2-2-200000000-2-2-2-222220000000000000000000000000000
χ202222-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2-222-2-2220000000000000000000000000000
χ212-22-22i2i−2i−2i02202-2-2-22-22i2i−2i−2i2i2i−2i−2i0000000000000000002i−2i2-200000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ222-22-22i2i−2i−2i02202-2-2-22-22i2i−2i−2i2i2i−2i−2i0000000000000000002i−2i2-20000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ232-22-22i2i−2i−2i02202-2-2-22-22i2i−2i−2i2i2i−2i−2i000000000000000000−2i2i-2200000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i
χ242-22-22i2i−2i−2i02202-2-2-22-22i2i−2i−2i2i2i−2i−2i000000000000000000−2i2i-220000000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i
χ252-22-2−2i−2i2i2i02202-2-2-22-2−2i−2i2i2i−2i−2i2i2i0000000000000000002i−2i-2200000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i
χ262-22-2−2i−2i2i2i02202-2-2-22-2−2i−2i2i2i−2i−2i2i2i0000000000000000002i−2i-220000000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i
χ272-22-2−2i−2i2i2i02202-2-2-22-2−2i−2i2i2i−2i−2i2i2i000000000000000000−2i2i2-200000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ282-22-2−2i−2i2i2i02202-2-2-22-2−2i−2i2i2i−2i−2i2i2i000000000000000000−2i2i2-20000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ292-2-222i−2i2i−2i0220-22-2-2-222i−2i2i−2i2i−2i2i−2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-200002i−2i00000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ302-2-222i−2i2i−2i0220-22-2-2-222i−2i2i−2i2i−2i2i−2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-200002i−2i0000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ312-2-222i−2i2i−2i0220-22-2-2-222i−2i2i−2i2i−2i2i−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000-220000−2i2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
χ322-2-222i−2i2i−2i0220-22-2-2-222i−2i2i−2i2i−2i2i−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000-220000−2i2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000
χ332-2-22−2i2i−2i2i0220-22-2-2-22−2i2i−2i2i−2i2i−2i2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-20000−2i2i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ342-2-22−2i2i−2i2i0220-22-2-2-22−2i2i−2i2i−2i2i−2i2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-20000−2i2i00000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ352-2-22−2i2i−2i2i0220-22-2-2-22−2i2i−2i2i−2i2i−2i2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000-2200002i−2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000
χ362-2-22−2i2i−2i2i0220-22-2-2-22−2i2i−2i2i−2i2i−2i2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000-2200002i−2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000
χ374444444441-24111-2-2-2-2-2-2-2111111-2-211-2-22222222200000000000000000000-1-1-1-1-1-1-1-100000000
χ384444444441-24111-2-2-2-2-2-2-2111111-2-211-2-2-2-2-2-2-2-2-2-2000000000000000000001111111100000000
χ39444444444-214-2-2-21111111-2-2-2-2-2-211-2-21100000000000000002222-1-1-1-1-1-1-1-10000000000000000
χ40444444444-214-2-2-21111111-2-2-2-2-2-211-2-2110000000000000000-2-2-2-2111111110000000000000000
χ4144444444-41-2-4111-2-2-2-2-2-2-21111-1-122-1-1222222-2-2-2-200000000000000000000-1-1-1-1111100000000
χ4244444444-41-2-4111-2-2-2-2-2-2-21111-1-122-1-122-2-2-2-22222000000000000000000001111-1-1-1-100000000
χ4344444444-4-21-4-2-2-21111111-2-2-2-222-1-122-1-1000000000000000022-2-2-1-1-1-111110000000000000000
χ4444444444-4-21-4-2-2-21111111-2-2-2-222-1-122-1-10000000000000000-2-2221111-1-1-1-10000000000000000
χ454444-4-4-4-441-2-4111-2-2-22222-1-1-1-111-2-2-1-1222i2i−2i−2i2i2i−2i−2i00000000000000000000−i−iii−i−iii00000000
χ464444-4-4-4-441-2-4111-2-2-22222-1-1-1-111-2-2-1-122−2i−2i2i2i−2i−2i2i2i00000000000000000000ii−i−iii−i−i00000000
χ474444-4-4-4-44-21-4-2-2-2111-1-1-1-12222-2-21122-1-100000000000000002-22-2-1-111-1-1110000000000000000
χ484444-4-4-4-44-21-4-2-2-2111-1-1-1-12222-2-21122-1-10000000000000000-22-2211-1-111-1-10000000000000000
χ494444-4-4-4-4-41-24111-2-2-22222-1-1-1-1-1-12211-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000−i−iiiii−i−i00000000
χ504444-4-4-4-4-41-24111-2-2-22222-1-1-1-1-1-12211-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000ii−i−i−i−iii00000000
χ514444-4-4-4-4-4-214-2-2-2111-1-1-1-1222222-1-1-2-21100000000000000002-2-22-1-11111-1-10000000000000000
χ524444-4-4-4-4-4-214-2-2-2111-1-1-1-1222222-1-1-2-2110000000000000000-222-211-1-1-1-1110000000000000000
χ5344-4-44-4-440440-4-444-4-44-4-444-4-440000000000000000000000000000000000000000000000000000
χ5444-4-44-4-440-21022-21-1-11-1-11-222-2003-3003-3000000000000000000003−33−33−33−30000000000000000
χ5544-4-44-4-440-21022-21-1-11-1-11-222-2003-3003-300000000000000000000−33−33−33−330000000000000000
χ5644-4-44-4-440-21022-21-1-11-1-11-222-200-3300-33000000000000000000003−33−3−33−330000000000000000
χ5744-4-44-4-440-21022-21-1-11-1-11-222-200-3300-3300000000000000000000−33−333−33−30000000000000000
χ5844-4-4-444-40440-4-444-4-4-444-4-444-40000000000000000000000000000000000000000000000000000
χ5944-4-4-444-40-21022-21-1-1-111-12-2-22003-300-33000000000000000000003−3−333−3−330000000000000000
χ6044-4-4-444-40-21022-21-1-1-111-12-2-22003-300-3300000000000000000000−333−3−333−30000000000000000
χ6144-4-4-444-40-21022-21-1-1-111-12-2-2200-33003-3000000000000000000003−3−33−333−30000000000000000
χ6244-4-4-444-40-21022-21-1-1-111-12-2-2200-33003-300000000000000000000−333−33−3−330000000000000000
χ634-4-444i−4i4i−4i01-20-11-122-2−2i2i−2i2ii−ii−i3-3003i−3i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1300000000
χ644-4-444i−4i4i−4i01-20-11-122-2−2i2i−2i2ii−ii−i3-3003i−3i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1300000000
χ654-4-444i−4i4i−4i01-20-11-122-2−2i2i−2i2ii−ii−i-3300−3i3i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1300000000
χ664-4-444i−4i4i−4i01-20-11-122-2−2i2i−2i2ii−ii−i-3300−3i3i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1300000000
χ674-4-44−4i4i−4i4i01-20-11-122-22i−2i2i−2i−ii−ii3-300−3i3i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2300000000
χ684-4-44−4i4i−4i4i01-20-11-122-22i−2i2i−2i−ii−ii3-300−3i3i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2300000000
χ694-4-44−4i4i−4i4i01-20-11-122-22i−2i2i−2i−ii−ii-33003i−3i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2300000000
χ704-4-44−4i4i−4i4i01-20-11-122-22i−2i2i−2i−ii−ii-33003i−3i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2300000000
χ7188-8-88-8-8802-40-2-22-444-444-42-2-220000000000000000000000000000000000000000000000000000
χ7288-8-8-888-802-40-2-22-4444-4-44-222-20000000000000000000000000000000000000000000000000000
χ738-88-88i8i−8i−8i02-402-2-24-44−4i−4i4i4i2i2i−2i−2i0000000000000000000000000000000000000000000000000000
χ748-88-88i8i−8i−8i0-420-444-22-22i2i−2i−2i−4i−4i4i4i0000000000000000000000000000000000000000000000000000
χ758-88-8−8i−8i8i8i02-402-2-24-444i4i−4i−4i−2i−2i2i2i0000000000000000000000000000000000000000000000000000
χ768-88-8−8i−8i8i8i0-420-444-22-2−2i−2i2i2i4i4i−4i−4i0000000000000000000000000000000000000000000000000000
χ778-8-888i−8i8i−8i0-4204-44-2-222i−2i2i−2i−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ788-8-88−8i8i−8i8i0-4204-44-2-22−2i2i−2i2i4i−4i4i−4i0000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.