Finite Group Databasebeta

← Group #11774066

Character table — Group #11774066

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222244444444444444444444888888121212121212121212121212121212121212121212121212181818182424242436364848484872727272
order12224444443366666612121212121212121212121212121212121288888888242424242424242424242424242424242244444444121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ5111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-11-111-1-1ii−i−i
χ6111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1111-1-1-111−i−iii
χ7111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-11-111-1-1−i−iii
χ8111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1111-1-1-111ii−i−i
χ91111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-11-11-1-111-11-1i−ii−i
χ101111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1-11-11-11-11-11−ii−ii
χ111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-11-11-1-111-11-1−ii−ii
χ121111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1-11-11-11-11-11i−ii−i
χ131111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-11-1-11-1-111-1-11
χ141111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-111-1-1-1-111-1-111-1
χ151111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-111111-1-11-1-11-1-11-111-1
χ161111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-11111-111-1-1-1-111-11-1-11
χ17222222222222222222222222222222222222000000000000000000000000-2-2-2-20000-2-200000000
χ18222222-2-2-2-2222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000-2-2220000-2200000000
χ192222-2-222-2-222222222-2-2-2-22222-2-2-2-2-2-222-2-2000000000000000000000000-2-22200002-200000000
χ202222-2-2-2-22222222222-2-2-2-2-2-2-2-22222-2-2-2-222000000000000000000000000-2-2-2-200002200000000
χ212-22-200002i−2i222-2-2-22-2000000002i2i−2i−2i00002i−2i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ2300002-22i−2i00000000000000
χ222-22-200002i−2i222-2-2-22-2000000002i2i−2i−2i00002i−2i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300002-22i−2i00000000000000
χ232-22-200002i−2i222-2-2-22-2000000002i2i−2i−2i00002i−2i2ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ2300000000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13-22−2i2i00000000000000
χ242-22-200002i−2i222-2-2-22-2000000002i2i−2i−2i00002i−2i−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23000000002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13-22−2i2i00000000000000
χ252-22-20000−2i2i222-2-2-22-200000000−2i−2i2i2i0000−2i2i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300002-2−2i2i00000000000000
χ262-22-20000−2i2i222-2-2-22-200000000−2i−2i2i2i0000−2i2i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ1300002-2−2i2i00000000000000
χ272-22-20000−2i2i222-2-2-22-200000000−2i−2i2i2i0000−2i2i−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13000000002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23-222i−2i00000000000000
χ282-22-20000−2i2i222-2-2-22-200000000−2i−2i2i2i0000−2i2i2ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ1300000000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23-222i−2i00000000000000
χ2944444444441-2111-2-2-2111111111111-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ3044444444441-2111-2-2-2111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111111111000000000000000000
χ314444444444-21-2-2-2111-2-2-2-2-2-2-2-2-2-2-2-21111110000000000000000000000000000222200-1-1-1-10000
χ324444444444-21-2-2-2111-2-2-2-2-2-2-2-2-2-2-2-21111110000000000000000000000000000-2-2-2-20011110000
χ33444444-4-4-4-41-2111-2-2-21111-1-1-1-1-1-1-1-1-2-222222i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii000000000000000000
χ34444444-4-4-4-41-2111-2-2-21111-1-1-1-1-1-1-1-1-2-22222−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i000000000000000000
χ35444444-4-4-4-4-21-2-2-2111-2-2-2-22222222211-1-1-1-1000000000000000000000000000022-2-200-1-1110000
χ36444444-4-4-4-4-21-2-2-2111-2-2-2-22222222211-1-1-1-10000000000000000000000000000-2-2220011-1-10000
χ374444-4-444-4-41-2111-2-2-2-1-1-1-11111-1-1-1-122-2-2222i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000000000
χ384444-4-444-4-41-2111-2-2-2-1-1-1-11111-1-1-1-122-2-222−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000000000
χ394444-4-444-4-4-21-2-2-21112222-2-2-2-22222-1-111-1-100000000000000000000000000002-22-200-11-110000
χ404444-4-444-4-4-21-2-2-21112222-2-2-2-22222-1-111-1-10000000000000000000000000000-22-22001-11-10000
χ414444-4-4-4-4441-2111-2-2-2-1-1-1-1-1-1-1-111112222-2-222-2-2-2-222-1-1-1-111111111-1-1-1-1000000000000000000
χ424444-4-4-4-4441-2111-2-2-2-1-1-1-1-1-1-1-111112222-2-2-2-22222-2-21111-1-1-1-1-1-1-1-11111000000000000000000
χ434444-4-4-4-444-21-2-2-211122222222-2-2-2-2-1-1-1-11100000000000000000000000000002-2-2200-111-10000
χ444444-4-4-4-444-21-2-2-211122222222-2-2-2-2-1-1-1-1110000000000000000000000000000-222-2001-1-110000
χ4544-4-44-400001-2-11-1-22211-1-13i3i−3i−3i3i−3i3i−3i2-2000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000000
χ4644-4-44-400001-2-11-1-22211-1-13i3i−3i−3i3i−3i3i−3i2-2000000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000000000
χ4744-4-44-400001-2-11-1-22211-1-1−3i−3i3i3i−3i3i−3i3i2-2000000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000000000000000
χ4844-4-44-400001-2-11-1-22211-1-1−3i−3i3i3i−3i3i−3i3i2-2000000000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000000000000000
χ4944-4-44-4000044-44-44-4-444-4-400000000-440000000000000000000000000000000000000000000000
χ5044-4-4-4400001-2-11-1-222-1-1113i3i−3i−3i−3i3i−3i3i-22000000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000000000000000
χ5144-4-4-4400001-2-11-1-222-1-1113i3i−3i−3i−3i3i−3i3i-22000000000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000000000000000
χ5244-4-4-4400001-2-11-1-222-1-111−3i−3i3i3i3i−3i3i−3i-22000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000000
χ5344-4-4-4400001-2-11-1-222-1-111−3i−3i3i3i3i−3i3i−3i-22000000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000000000
χ5444-4-4-44000044-44-44-4-4-4-444000000004-40000000000000000000000000000000000000000000000
χ554-44-400004i−4i1-21-1-12-223i−3i3i−3i3-33-3ii−i−i0000−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13000000000000000000
χ564-44-400004i−4i1-21-1-12-223i−3i3i−3i3-33-3ii−i−i0000−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13000000000000000000
χ574-44-400004i−4i1-21-1-12-22−3i3i−3i3i-33-33ii−i−i0000−2i2i2ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13000000000000000000
χ584-44-400004i−4i1-21-1-12-22−3i3i−3i3i-33-33ii−i−i0000−2i2i−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13000000000000000000
χ594-44-40000−4i4i1-21-1-12-223i−3i3i−3i-33-33−i−iii00002i−2i−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23000000000000000000
χ604-44-40000−4i4i1-21-1-12-223i−3i3i−3i-33-33−i−iii00002i−2i2ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23000000000000000000
χ614-44-40000−4i4i1-21-1-12-22−3i3i−3i3i3-33-3−i−iii00002i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23000000000000000000
χ624-44-40000−4i4i1-21-1-12-22−3i3i−3i3i3-33-3−i−iii00002i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23000000000000000000
χ634-4-44004i−4i001-2-1-1122-23i−3i−3i3ii−i−ii-333-3002i−2i0000000000−i3i3i3−i3−333−3−333−3i3−i3−i3i3000000000000000000
χ644-4-44004i−4i001-2-1-1122-23i−3i−3i3ii−i−ii-333-3002i−2i0000000000i3−i3−i3i33−3−333−3−33−i3i3i3−i3000000000000000000
χ654-4-44004i−4i001-2-1-1122-2−3i3i3i−3ii−i−ii3-3-33002i−2i00000000003−3−33i3−i3−i3i3−i3i3i3−i33−3−33000000000000000000
χ664-4-44004i−4i001-2-1-1122-2−3i3i3i−3ii−i−ii3-3-33002i−2i0000000000−333−3−i3i3i3−i3i3−i3−i3i3−333−3000000000000000000
χ674-4-44004i−4i0044-4-44-4-4400004i−4i−4i4i000000−4i4i00000000000000000000000000000000000000000000
χ684-4-4400−4i4i001-2-1-1122-23i−3i−3i3i−iii−i3-3-3300−2i2i00000000003−3−33−i3i3i3−i3i3−i3−i3i33−3−33000000000000000000
χ694-4-4400−4i4i001-2-1-1122-23i−3i−3i3i−iii−i3-3-3300−2i2i0000000000−333−3i3−i3−i3i3−i3i3i3−i3−333−3000000000000000000
χ704-4-4400−4i4i001-2-1-1122-2−3i3i3i−3i−iii−i-333-300−2i2i0000000000−i3i3i3−i33−3−333−3−33i3−i3−i3i3000000000000000000
χ714-4-4400−4i4i001-2-1-1122-2−3i3i3i−3i−iii−i-333-300−2i2i0000000000i3−i3−i3i3−333−3−333−3−i3i3i3−i3000000000000000000
χ724-4-4400−4i4i0044-4-44-4-440000−4i4i4i−4i0000004i−4i00000000000000000000000000000000000000000000
χ7388-8-88-80000-424-442-2-2-4-44400000000-220000000000000000000000000000000000000000000000
χ7488-8-8-880000-424-442-2-244-4-4000000002-20000000000000000000000000000000000000000000000
χ758-88-800008i−8i-42-444-22-200000000−4i−4i4i4i00002i−2i000000000000000000000000000000000000000000
χ768-88-80000−8i8i-42-444-22-2000000004i4i−4i−4i0000−2i2i000000000000000000000000000000000000000000
χ778-8-88008i−8i00-4244-4-2-220000−4i4i4i−4i000000−2i2i00000000000000000000000000000000000000000000
χ788-8-8800−8i8i00-4244-4-2-2200004i−4i−4i4i0000002i−2i00000000000000000000000000000000000000000000

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