Finite Group Databasebeta

← Group #10896448

Character table — Group #10896448

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888121212121212121212121212161616161616161616162424242424244848
order124422234446888812126668812121224242424448888881212121224242424242444448888888888242424242424242422444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111
χ9111111111111-1-1-1-111111-1-1111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-111-1-111-1-11-11-1111-1
χ10111111111111-1-1-1-111111-1-1111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111111-111-1-111-1-1-11-11-1-1-11
χ11111111111111-1-1-1-111111-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111-1-111-11-1111-11
χ12111111111111-1-1-1-111111-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-11-1-111-1-1111-11-1-1-11-1
χ13111111111111-1-1-1-111111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1111-1-1-1-111-11-11-1-11-1
χ14111111111111-1-1-1-111111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1111-1-1-1-1111-11-111-11
χ15111111111111-1-1-1-111111-1-1111-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111-1-1-1-111111-1-1-11111-1-11-11-1-1-1-11
χ16111111111111-1-1-1-111111-1-1111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11-1-1-11111-1-1-11-11111-1
χ172222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1-1-1-1-100000000
χ182222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1000000000000-2-21111111100000000
χ192222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1000000000000-2-2-1-1-1-1111100000000
χ202222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-1000000000000221111-1-1-1-100000000
χ212222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-1-1-1111122-2-222-2-2-1-1-1-11111110000000000002-2-1-111-1-11100000000
χ222222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-1-1-1111122-2-2-2-222-1-1-1-1111111000000000000-2211-1-111-1-100000000
χ232222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-1-1-11111-2-22222-2-21111-1-1-1-111000000000000-22-1-11111-1-100000000
χ242222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-1-1-11111-2-222-2-2221111-1-1-1-1110000000000002-211-1-1-1-11100000000
χ252222-2-222-22-22222222-2-22-2-2-22-222220000000000000000-2-20000000022-2-2000000000000002-200
χ262222-2-222-22-22222222-2-22-2-2-22-222220000000000000000-2-200000000-2-22200000000000000-2200
χ272222-2-222-22-22-2-2-2-222-2-2222-22-2-2-2-2-20000000000000000220000000022-2-200000000000000-2200
χ282222-2-222-22-22-2-2-2-222-2-2222-22-2-2-2-2-200000000000000002200000000-2-222000000000000002-200
χ2922-2-22222-2-2-220000-2-222200-2-2-200002-200000022-2-200000000002i2i−2i−2i2i−2i2i−2i000000000000000000
χ3022-2-22222-2-2-220000-2-222200-2-2-200002-200000022-2-20000000000−2i−2i2i2i−2i2i−2i2i000000000000000000
χ3122-2-22222-2-2-220000-2-222200-2-2-20000-22000000-2-22200000000002i2i−2i−2i−2i2i−2i2i000000000000000000
χ3222-2-22222-2-2-220000-2-222200-2-2-20000-22000000-2-2220000000000−2i−2i2i2i2i−2i2i−2i000000000000000000
χ3322-2-22-2-2222-2222-2-2-2-22-2-22-222-222-2-200000000000000002-2000000000000000000000022-2-20000
χ3422-2-22-2-2222-2222-2-2-2-22-2-22-222-222-2-200000000000000002-20000000000000000000000-2-2220000
χ3522-2-22-2-2222-22-2-222-2-22-2-2-2222-2-2-2220000000000000000-2200000000000000000000002-2-220000
χ3622-2-22-2-2222-22-2-222-2-22-2-2-2222-2-2-2220000000000000000-220000000000000000000000-222-20000
χ3722-2-2-22-22-222222-2-2-2-2-22-2-22-22222-2-200002i−2i2i−2i00000000-22000000000000002i−2i2i−2i000000000000
χ3822-2-2-22-22-222222-2-2-2-2-22-2-22-22222-2-20000−2i2i−2i2i00000000-2200000000000000−2i2i−2i2i000000000000
χ3922-2-2-22-22-2222-2-222-2-2-22-22-2-222-2-22200002i−2i−2i2i000000002-2000000000000002i−2i−2i2i000000000000
χ4022-2-2-22-22-2222-2-222-2-2-22-22-2-222-2-2220000−2i2i2i−2i000000002-200000000000000−2i2i2i−2i000000000000
χ4122-2-2-22-2-1-222-122-2-2111-11-221-1-1-1-11100002i−2i2i−2i3−33−333−3−31-100000000000000−ii−ii−i3i3−i3i300000000
χ4222-2-2-22-2-1-222-122-2-2111-11-221-1-1-1-11100002i−2i2i−2i−33−33−3−3331-100000000000000−ii−iii3−i3i3−i300000000
χ4322-2-2-22-2-1-222-122-2-2111-11-221-1-1-1-1110000−2i2i−2i2i3−33−333−3−31-100000000000000i−ii−ii3−i3i3−i300000000
χ4422-2-2-22-2-1-222-122-2-2111-11-221-1-1-1-1110000−2i2i−2i2i−33−33−3−3331-100000000000000i−ii−i−i3i3−i3i300000000
χ4522-2-2-22-2-1-222-1-2-222111-112-21-1-111-1-100002i−2i−2i2i3−33−3−3−333-1100000000000000−iii−i−i3i3i3−i300000000
χ4622-2-2-22-2-1-222-1-2-222111-112-21-1-111-1-100002i−2i−2i2i−33−3333−3−3-1100000000000000−iii−ii3−i3−i3i300000000
χ4722-2-2-22-2-1-222-1-2-222111-112-21-1-111-1-10000−2i2i2i−2i3−33−3−3−333-1100000000000000i−i−iii3−i3−i3i300000000
χ4822-2-2-22-2-1-222-1-2-222111-112-21-1-111-1-10000−2i2i2i−2i−33−3333−3−3-1100000000000000i−i−ii−i3i3i3−i300000000
χ4922-2-2-2-2222-2220000-2-2-2-22002-220000002i−2i000000002i−2i2i−2i0022-2-200002i−2i−2i2i000000000000000000
χ5022-2-2-2-2222-2220000-2-2-2-22002-220000002i−2i000000002i−2i2i−2i00-2-2220000−2i2i2i−2i000000000000000000
χ5122-2-2-2-2222-2220000-2-2-2-22002-22000000−2i2i00000000−2i2i−2i2i0022-2-20000−2i2i2i−2i000000000000000000
χ5222-2-2-2-2222-2220000-2-2-2-22002-22000000−2i2i00000000−2i2i−2i2i00-2-22200002i−2i−2i2i000000000000000000
χ5344444-4-44-4-4440000444-4-400-4-440000000000000000000000000000000000000000000000000000
χ5444444-4-4-2-4-44-20000-2-2-2220022-20000000000000000−2i32i32i3−2i300000000000000000000000000000000
χ5544444-4-4-2-4-44-20000-2-2-2220022-200000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ564444-44-444-4-44000044-44-4004-4-40000000000000000000000000000000000000000000000000000
χ574444-44-4-24-4-4-20000-2-22-2200-22200000000000023−23−2323000000000000000000000000000000000000
χ584444-44-4-24-4-4-20000-2-22-2200-222000000000000−232323−23000000000000000000000000000000000000
χ594444-4-44-2-44-4-24444-2-222-2-4-42-22-2-2-2-2000000000000000022000000000000000000000000000000
χ604444-4-44-2-44-4-2-4-4-4-4-2-222-2442-2222220000000000000000-2-2000000000000000000000000000000
χ6144-4-4444-2-4-4-4-2000022-2-2-20022200004-4000000-2-222000000000000000000000000000000000000
χ6244-4-4444-2-4-4-4-2000022-2-2-2002220000-4400000022-2-2000000000000000000000000000000000000
χ6344-4-44-4-4-244-4-244-4-422-2224-4-2-22-2-2220000000000000000-22000000000000000000000000000000
χ6444-4-44-4-4-244-4-2-4-44422-222-44-2-2222-2-200000000000000002-2000000000000000000000000000000
χ6544-4-4-4-44-24-44-200002222-200-22-20000004i−4i00000000−2i2i−2i2i00000000000000000000000000000000
χ6644-4-4-4-44-24-44-200002222-200-22-2000000−4i4i000000002i−2i2i−2i00000000000000000000000000000000
χ674-44i−4i0004000-422−22−2i22i24i−4i0000000022−22−2i22i20000000000000000002-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000
χ684-44i−4i0004000-422−22−2i22i24i−4i0000000022−22−2i22i2000000000000000000-22−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000
χ694-44i−4i0004000-4−22222i2−2i24i−4i00000000−22222i2−2i20000000000000000002-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000
χ704-44i−4i0004000-4−22222i2−2i24i−4i00000000−22222i2−2i2000000000000000000-22−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000
χ714-4−4i4i0004000-422−222i2−2i2−4i4i0000000022−222i2−2i20000000000000000002-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000
χ724-4−4i4i0004000-422−222i2−2i2−4i4i0000000022−222i2−2i2000000000000000000-222i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000
χ734-4−4i4i0004000-4−2222−2i22i2−4i4i00000000−2222−2i22i20000000000000000002-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000
χ744-4−4i4i0004000-4−2222−2i22i2−4i4i00000000−2222−2i22i2000000000000000000-222i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000
χ758-88i−8i000-4000442−42−4i24i2−4i4i00000000−22222i2−2i2000000000000000000000000000000000000000000000000
χ768-88i−8i000-40004−42424i2−4i2−4i4i0000000022−22−2i22i2000000000000000000000000000000000000000000000000
χ778-8−8i8i000-4000442−424i2−4i24i−4i00000000−2222−2i22i2000000000000000000000000000000000000000000000000
χ788-8−8i8i000-40004−4242−4i24i24i−4i0000000022−222i2−2i2000000000000000000000000000000000000000000000000

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