Finite Group Databasebeta

← Group #11774481

Character table — Group #11774481

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111444444444444444444888888881212121212121212181818181818181824242424242424242424242424242424242424243636363636363636
order122244443344666666121212121212121212121212121212128888888822444444244466121212121212242424242424242488888888
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
χ51111111111-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ71111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ81111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1111-1111111-1-1-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−i1111-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-1111-1111111-1-1-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−i1111-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ111111-1-1-1-1111-1111111-1-1-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii1111-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ121111-1-1-1-1111-1111111-1-1-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii1111-1-1-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii-1-11111-1-11-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii-1-11111-1-1-111-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ151111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i-1-11111-1-11-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ161111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i-1-11111-1-1-111-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222-2-222222222222222-2-2-2-2-2-2-2-20000000022-2-222-2-20000000000000000000000000000
χ192222-2-2-2-2222-2222222-2-2-2-2-2-2-2-222-2-222-2-200000000-2-2-2-222220000000000000000000000000000
χ202222-2-2-2-222-22222222-2-2-2-2-2-2-2-2-2-222-2-2220000000022-2-2-2-2220000000000000000000000000000
χ2122-2-22i−2i2i−2i22002-2-22-2-22i−2i2i2i−2i−2i2i−2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13002-2002i−2i00000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ2222-2-22i−2i2i−2i22002-2-22-2-22i−2i2i2i−2i−2i2i−2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13002-2002i−2i0000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ2322-2-22i−2i2i−2i22002-2-22-2-22i−2i2i2i−2i−2i2i−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000-2200−2i2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
χ2422-2-22i−2i2i−2i22002-2-22-2-22i−2i2i2i−2i−2i2i−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000-2200−2i2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000
χ2522-2-2−2i2i−2i2i22002-2-22-2-2−2i2i−2i−2i2i2i−2i2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23002-200−2i2i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ2622-2-2−2i2i−2i2i22002-2-22-2-2−2i2i−2i−2i2i2i−2i2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23002-200−2i2i00000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ2722-2-2−2i2i−2i2i22002-2-22-2-2−2i2i−2i−2i2i2i−2i2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000-22002i−2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000
χ2822-2-2−2i2i−2i2i22002-2-22-2-2−2i2i−2i−2i2i2i−2i2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000-22002i−2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000
χ292-22-22i−2i−2i2i2200-22-2-22-22i−2i2i−2i2i−2i−2i2i00000000000000002-2002i−2i00000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ302-22-22i−2i−2i2i2200-22-2-22-22i−2i2i−2i2i−2i−2i2i00000000000000002-2002i−2i0000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ312-22-22i−2i−2i2i2200-22-2-22-22i−2i2i−2i2i−2i−2i2i0000000000000000-2200−2i2i00000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ322-22-22i−2i−2i2i2200-22-2-22-22i−2i2i−2i2i−2i−2i2i0000000000000000-2200−2i2i0000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ332-22-2−2i2i2i−2i2200-22-2-22-2−2i2i−2i2i−2i2i2i−2i00000000000000002-200−2i2i00000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ342-22-2−2i2i2i−2i2200-22-2-22-2−2i2i−2i2i−2i2i2i−2i00000000000000002-200−2i2i0000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ352-22-2−2i2i2i−2i2200-22-2-22-2−2i2i−2i2i−2i2i2i−2i0000000000000000-22002i−2i00000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ362-22-2−2i2i2i−2i2200-22-2-22-2−2i2i−2i2i−2i2i2i−2i0000000000000000-22002i−2i0000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ37444444441-244111-2-2-211-2-2-2-2111111-2-2-2-22222222200000000000000000000-1-1-1-1-1-1-1-100000000
χ38444444441-244111-2-2-211-2-2-2-2111111-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000001111111100000000
χ39444444441-2-4-4111-2-2-211-2-2-2-211-1-1-1-122222222-2-2-2-200000000000000000000-1-1-1-1111100000000
χ40444444441-2-4-4111-2-2-211-2-2-2-211-1-1-1-12222-2-2-2-22222000000000000000000001111-1-1-1-100000000
χ4144444444-2144-2-2-2111-2-21111-2-2-2-2-2-2111100000000000000002222-1-1-1-1-1-1-1-10000000000000000
χ4244444444-2144-2-2-2111-2-21111-2-2-2-2-2-211110000000000000000-2-2-2-2111111110000000000000000
χ4344444444-21-4-4-2-2-2111-2-21111-2-22222-1-1-1-1000000000000000022-2-2-1-1-1-111110000000000000000
χ4444444444-21-4-4-2-2-2111-2-21111-2-22222-1-1-1-10000000000000000-2-2221111-1-1-1-10000000000000000
χ454444-4-4-4-41-24-4111-2-2-2-1-12222-1-111-1-1-2-2222i2i−2i−2i2i2i−2i−2i00000000000000000000−i−iii−i−iii00000000
χ464444-4-4-4-41-24-4111-2-2-2-1-12222-1-111-1-1-2-222−2i−2i2i2i−2i−2i2i2i00000000000000000000ii−i−iii−i−i00000000
χ474444-4-4-4-41-2-44111-2-2-2-1-12222-1-1-1-11122-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000−i−iiiii−i−i00000000
χ484444-4-4-4-41-2-44111-2-2-2-1-12222-1-1-1-11122-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000ii−i−i−i−iii00000000
χ494444-4-4-4-4-214-4-2-2-211122-1-1-1-122-2-22211-1-100000000000000002-22-2-1-111-1-1110000000000000000
χ504444-4-4-4-4-214-4-2-2-211122-1-1-1-122-2-22211-1-10000000000000000-22-2211-1-111-1-10000000000000000
χ514444-4-4-4-4-21-44-2-2-211122-1-1-1-12222-2-2-1-11100000000000000002-2-22-1-11111-1-10000000000000000
χ524444-4-4-4-4-21-44-2-2-211122-1-1-1-12222-2-2-1-1110000000000000000-222-211-1-1-1-1110000000000000000
χ5344-4-44i−4i4i−4i1-2001-1-1-222i−i−2i−2i2i2ii−i3-33i−3i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1300000000
χ5444-4-44i−4i4i−4i1-2001-1-1-222i−i−2i−2i2i2ii−i3-33i−3i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1300000000
χ5544-4-44i−4i4i−4i1-2001-1-1-222i−i−2i−2i2i2ii−i-33−3i3i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1300000000
χ5644-4-44i−4i4i−4i1-2001-1-1-222i−i−2i−2i2i2ii−i-33−3i3i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1300000000
χ5744-4-4−4i4i−4i4i1-2001-1-1-222−ii2i2i−2i−2i−ii3-3−3i3i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2300000000
χ5844-4-4−4i4i−4i4i1-2001-1-1-222−ii2i2i−2i−2i−ii3-3−3i3i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2300000000
χ5944-4-4−4i4i−4i4i1-2001-1-1-222−ii2i2i−2i−2i−ii-333i−3i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2300000000
χ6044-4-4−4i4i−4i4i1-2001-1-1-222−ii2i2i−2i−2i−ii-333i−3i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2300000000
χ614-4-4444-4-44400-4-44-4-44444-4-44-4-40000000000000000000000000000000000000000000000000000
χ624-4-4444-4-4-210022-2-1-11-2-21-1-112200003i−3i3i−3i00000000000000000000−i3i3−i3i33−33−30000000000000000
χ634-4-4444-4-4-210022-2-1-11-2-21-1-112200003i−3i3i−3i00000000000000000000i3−i3i3−i3−33−330000000000000000
χ644-4-4444-4-4-210022-2-1-11-2-21-1-11220000−3i3i−3i3i00000000000000000000−i3i3−i3i3−33−330000000000000000
χ654-4-4444-4-4-210022-2-1-11-2-21-1-11220000−3i3i−3i3i00000000000000000000i3−i3i3−i33−33−30000000000000000
χ664-4-44-4-4444400-4-44-4-44-4-4-444-4440000000000000000000000000000000000000000000000000000
χ674-4-44-4-444-210022-2-1-1122-111-1-2-200003i−3i−3i3i00000000000000000000−i3i3i3−i33−3−330000000000000000
χ684-4-44-4-444-210022-2-1-1122-111-1-2-200003i−3i−3i3i00000000000000000000i3−i3−i3i3−333−30000000000000000
χ694-4-44-4-444-210022-2-1-1122-111-1-2-20000−3i3i3i−3i00000000000000000000−i3i3i3−i3−333−30000000000000000
χ704-4-44-4-444-210022-2-1-1122-111-1-2-20000−3i3i3i−3i00000000000000000000i3−i3−i3i33−3−330000000000000000
χ7188-8-88i−8i8i−8i-4200-4442-2-2−4i4i2i2i−2i−2i−4i4i0000000000000000000000000000000000000000000000000000
χ7288-8-8−8i8i−8i8i-4200-4442-2-24i−4i−2i−2i2i2i4i−4i0000000000000000000000000000000000000000000000000000
χ738-88-88i−8i−8i8i2-400-22-24-442i−2i−4i4i−4i4i−2i2i0000000000000000000000000000000000000000000000000000
χ748-88-88i−8i−8i8i-42004-44-22-2−4i4i2i−2i2i−2i4i−4i0000000000000000000000000000000000000000000000000000
χ758-88-8−8i8i8i−8i2-400-22-24-44−2i2i4i−4i4i−4i2i−2i0000000000000000000000000000000000000000000000000000
χ768-88-8−8i8i8i−8i-42004-44-22-24i−4i−2i2i−2i2i−4i4i0000000000000000000000000000000000000000000000000000
χ778-8-8888-8-82-400-2-2244-422-444-4-2-20000000000000000000000000000000000000000000000000000
χ788-8-88-8-8882-400-2-2244-4-2-24-4-44220000000000000000000000000000000000000000000000000000

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