Finite Group Databasebeta

← Group #10840278

Character table — Group #10840278

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444466668888888888888888881212121212121616161616161616161624242424242424244848
order124422234446888812126668812121224242424444444444488121212122424242424244488888812121212242424242224448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1
χ31111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-111-111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111111111-1-1
χ9111111111111-1-1-1-111111-1-1111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-111-1-111-1-1-11-1-11-1111-1
χ10111111111111-1-1-1-111111-1-1111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-11-1-111-1-111-1-11-1-1111-11
χ11111111111111-1-1-1-111111-1-1111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-111-1-1-1-1-1111-1-1-1-11111-111-1-1-1-11
χ12111111111111-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11-1-1-11111-1-11-111-11-1-11-1
χ13111111111111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-111-1-11-111-11-1-1-11
χ14111111111111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-111-1-11111-111-1-1-11-1
χ15111111111111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1111-1-1-1-111-1-11-1-11111-1
χ16111111111111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-11111-1-1-11-1-11-111-11
χ172222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-1000022222222-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-10000000000
χ182222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-1000022-2-2-2-222-1-1-1-1-1-1-1-1-1-1000000-2-2111111110000000000
χ192222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-10000-2-22222-2-211111111-1-1000000-2-2-1-1-1-111110000000000
χ202222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-211111111-1-1000000221111-1-1-1-10000000000
χ212222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-1-1-1111100002222-2-2-2-2-1-1-1-11111110000002-2-1-111-1-1110000000000
χ222222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-1-1-11111000022-2-222-2-2-1-1-1-1111111000000-2211-1-111-1-10000000000
χ232222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-1-1-111110000-2-222-2-2221111-1-1-1-111000000-22-1-11111-1-10000000000
χ242222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-1-1-111110000-2-2-2-222221111-1-1-1-1110000002-211-1-1-1-1110000000000
χ2522222-2-22-22-22222222-22-2-2-2-22-222220000002i−2i2i−2i0000000000-2-2000000002i−2i2i−2i00000000000000
χ2622222-2-22-22-22222222-22-2-2-2-22-22222000000−2i2i−2i2i0000000000-2-200000000−2i2i−2i2i00000000000000
χ2722222-2-22-22-22-2-2-2-222-22-222-22-2-2-2-2-20000002i−2i−2i2i000000000022000000002i−2i−2i2i00000000000000
χ2822222-2-22-22-22-2-2-2-222-22-222-22-2-2-2-2-2000000−2i2i2i−2i00000000002200000000−2i2i2i−2i00000000000000
χ2922222-2-2-1-22-2-12222-1-11-11-2-21-11-1-1-1-10000002i−2i2i−2i00−i3−i3i3i3−i3−i3i3i31100000000−ii−ii3−33−30000000000
χ3022222-2-2-1-22-2-12222-1-11-11-2-21-11-1-1-1-10000002i−2i2i−2i00i3i3−i3−i3i3i3−i3−i31100000000−ii−ii−33−330000000000
χ3122222-2-2-1-22-2-12222-1-11-11-2-21-11-1-1-1-1000000−2i2i−2i2i00−i3−i3i3i3−i3−i3i3i31100000000i−ii−i−33−330000000000
χ3222222-2-2-1-22-2-12222-1-11-11-2-21-11-1-1-1-1000000−2i2i−2i2i00i3i3−i3−i3i3i3−i3−i31100000000i−ii−i3−33−30000000000
χ3322222-2-2-1-22-2-1-2-2-2-2-1-11-11221-1111110000002i−2i−2i2i00−i3−i3i3i3i3i3−i3−i3-1-100000000−iii−i3−3−330000000000
χ3422222-2-2-1-22-2-1-2-2-2-2-1-11-11221-1111110000002i−2i−2i2i00i3i3−i3−i3−i3−i3i3i3-1-100000000−iii−i−333−30000000000
χ3522222-2-2-1-22-2-1-2-2-2-2-1-11-11221-111111000000−2i2i2i−2i00−i3−i3i3i3i3i3−i3−i3-1-100000000i−i−ii−333−30000000000
χ3622222-2-2-1-22-2-1-2-2-2-2-1-11-11221-111111000000−2i2i2i−2i00i3i3−i3−i3−i3−i3i3i3-1-100000000i−i−ii3−3−330000000000
χ372222-22-222-2-22000022-2-22002-2-2000022222i−2i0000002i−2i2i−2i000000-2-2000000000000000000002i−2i00
χ382222-22-222-2-22000022-2-22002-2-200002222−2i2i000000−2i2i−2i2i000000-2-200000000000000000000−2i2i00
χ392222-22-222-2-22000022-2-22002-2-20000-2-2-2-22i−2i0000002i−2i2i−2i0000002200000000000000000000−2i2i00
χ402222-22-222-2-22000022-2-22002-2-20000-2-2-2-2−2i2i000000−2i2i−2i2i00000022000000000000000000002i−2i00
χ4122-2-22-2-222-2220000-2-2-22-2002-2200002i2i−2i−2i0000002i−2i00002i−2i2i−2i002i−2i00000000000000200-2000000
χ4222-2-22-2-222-2220000-2-2-22-2002-2200002i2i−2i−2i000000−2i2i0000−2i2i−2i2i002i−2i00000000000000-2002000000
χ4322-2-22-2-222-2220000-2-2-22-2002-220000−2i−2i2i2i0000002i−2i00002i−2i2i−2i00−2i2i00000000000000-2002000000
χ4422-2-22-2-222-2220000-2-2-22-2002-220000−2i−2i2i2i000000−2i2i0000−2i2i−2i2i00−2i2i00000000000000200-2000000
χ4522-2-2-22-22-222222-2-2-2-2-2-222-2-22222-2-2000000000000000000002-200000000000000000220-2-20000
χ4622-2-2-22-22-222222-2-2-2-2-2-222-2-22222-2-2000000000000000000002-200000000000000000-2-20220000
χ4722-2-2-22-22-2222-2-222-2-2-2-22-22-222-2-22200000000000000000000-22000000000000000002-20-220000
χ4822-2-2-22-22-2222-2-222-2-2-2-22-22-222-2-22200000000000000000000-2200000000000000000-2202-20000
χ4922-2-2-2-22222-2222-2-2-2-22-2-2-2222-222-2-22i2i−2i−2i0000000000000000-22−2i2i2i2i−2i−2i00000000000000000000
χ5022-2-2-2-22222-2222-2-2-2-22-2-2-2222-222-2-2−2i−2i2i2i0000000000000000-222i−2i−2i−2i2i2i00000000000000000000
χ5122-2-2-2-22222-22-2-222-2-22-2-22-222-2-2-2222i2i−2i−2i00000000000000002-2−2i2i−2i−2i2i2i00000000000000000000
χ5222-2-2-2-22222-22-2-222-2-22-2-22-222-2-2-222−2i−2i2i2i00000000000000002-22i−2i2i2i−2i−2i00000000000000000000
χ534444-44-4-24-4-4-20000-2-222-200-222000000004i−4i000000−2i2i−2i2i00000000000000000000000000000000
χ544444-44-4-24-4-4-20000-2-222-200-22200000000−4i4i0000002i−2i2i−2i00000000000000000000000000000000
χ554444-4-444-4-4440000444-4-400-4-440000000000000000000000000000000000000000000000000000
χ564444-4-44-2-4-44-20000-2-2-2220022-2000000000000000023−23−232300000000000000000000000000000000
χ574444-4-44-2-4-44-20000-2-2-2220022-20000000000000000−232323−2300000000000000000000000000000000
χ5844-4-44444-4-4-440000-4-444400-4-4-40000000000000000000000000000000000000000000000000000
χ5944-4-4444-2-4-4-4-2000022-2-2-2002220000000000000000000023−23−23230000000000000000000000000000
χ6044-4-4444-2-4-4-4-2000022-2-2-20022200000000000000000000−232323−230000000000000000000000000000
χ6144-4-44-4-4-24-44-20000222-2200-22-2000000000000004i−4i0000−2i2i−2i2i0000000000000000000000000000
χ6244-4-44-4-4-24-44-20000222-2200-22-200000000000000−4i4i00002i−2i2i−2i0000000000000000000000000000
χ6344-4-4-44-4-2-444-244-4-42222-24-42-2-2-2-22200000000000000000000-2200000000000000000000000000
χ6444-4-4-44-4-2-444-2-4-4442222-2-442-2-222-2-2000000000000000000002-200000000000000000000000000
χ6544-4-4-4-44-244-4-244-4-422-222-44-2-22-2-222000000000000000000002-200000000000000000000000000
χ6644-4-4-4-44-244-4-2-4-44422-2224-4-2-2222-2-200000000000000000000-2200000000000000000000000000
χ674-44i−4i0004000-422−22−2i22i24i−4i0000000022−22−2i22i22+2i−2−2i2−2i−2+2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ684-44i−4i0004000-422−22−2i22i24i−4i0000000022−22−2i22i2−2−2i2+2i−2+2i2−2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ694-44i−4i0004000-4−22222i2−2i24i−4i00000000−22222i2−2i22+2i−2−2i2−2i−2+2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ704-44i−4i0004000-4−22222i2−2i24i−4i00000000−22222i2−2i2−2−2i2+2i−2+2i2−2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ714-4−4i4i0004000-422−222i2−2i2−4i4i0000000022−222i2−2i22−2i−2+2i2+2i−2−2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ724-4−4i4i0004000-422−222i2−2i2−4i4i0000000022−222i2−2i2−2+2i2−2i−2−2i2+2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ734-4−4i4i0004000-4−2222−2i22i2−4i4i00000000−2222−2i22i22−2i−2+2i2+2i−2−2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ744-4−4i4i0004000-4−2222−2i22i2−4i4i00000000−2222−2i22i2−2+2i2−2i−2−2i2+2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
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.