Finite Group Databasebeta

← Group #10840272

Character table — Group #10840272

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444466668888888888888888881212121212121616161616161616161624242424242424244848
order124422234444444612124466612121212121212888822444466881212121212121212888888468121212242424242444448848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-11-11111-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ31111111111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-1111111-11-11-1-111-1-1-1-111-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111-11-111-1-111-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-11-11-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ7111111111111111111111111111111-1-1-1-1-11-11-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-11-111-1-11111111111-1-1
χ9111111111-1-1-1-111111-1-111111-1-1-1-1111111111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-11111-1-1-1-111-11
χ10111111111-1-1-1-111111-1-111111-1-1-1-1111111-11-1-1-1111111-1-1-1-1-1-111-1-1-1-11-1-1-11111-1-11111-1-1-1-11-1
χ11111111111-1-1-1-111111-1-111111-1-1-1-111111-11-1111-1-1-1-1-1-1-1-1111111-1-1-1-111-1111-1-1-1-1-1-1-1-111111-1
χ12111111111-1-1-1-111111-1-111111-1-1-1-111111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-11-1-1-11111-1-11111-1-1-11
χ13111111111-1-1-1-111111-1-111111-1-1-1-11-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-1-11111-1-11-1
χ14111111111-1-1-1-111111-1-111111-1-1-1-11-1-1-1-11-11-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-11111-1-1-1-1-1-11111-11
χ15111111111-1-1-1-111111-1-111111-1-1-1-11-1-1-1-1-11-1111-1-1-1-1-1-1-1-11111-1-1111111-1111-1-1-1-11111-1-1-1-1-11
χ16111111111-1-1-1-111111-1-111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111-1-11-1-1-1111111-1-1-1-1111-1
χ172222222-12222222-1-1-122-1-1-1-1-1-1-1-1-1-10000222222-1-122-1-1-1-1-1-1-1-10000002-12-1-1-1-1-1-1-10000000000
χ182222222-12222222-1-1-122-1-1-1-1-1-1-1-1-1-100002-22-222-1-1-2-2-1-1-1-1-1-1-1-1000000-21-211111110000000000
χ192222222-12222222-1-1-122-1-1-1-1-1-1-1-1-1-10000-22-22-2-2112211-1-11111000000-2-1-2-111-1-1110000000000
χ202222222-12222222-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-2-2-211-2-211-1-111110000002121-1-111-1-10000000000
χ212222222-12-2-2-2-222-1-1-1-2-2-1-1-1-1-11111-100002222-2-2-1-1-2-2-1-1111111000000-2-12-11111-1-10000000000
χ222222222-12-2-2-2-222-1-1-1-2-2-1-1-1-1-11111-100002-22-2-2-2-1-122-1-111111100000021-21-1-1-1-1110000000000
χ232222222-12-2-2-2-222-1-1-1-2-2-1-1-1-1-11111-10000-22-222211-2-21111-1-1-1-10000002-1-2-1-1-111110000000000
χ242222222-12-2-2-2-222-1-1-1-2-2-1-1-1-1-11111-10000-2-2-2-22211221111-1-1-1-1000000-212111-1-1-1-10000000000
χ2522222-2-22-200002-2222002-2-22-20000-2222200002i−2i000000002i2i−2i−2i-2-20000000000000000002i−2i0000
χ2622222-2-22-200002-2222002-2-22-20000-222220000−2i2i00000000−2i−2i2i2i-2-2000000000000000000−2i2i0000
χ2722222-2-22-200002-2222002-2-22-20000-2-2-2-2-200002i−2i000000002i2i−2i−2i22000000000000000000−2i2i0000
χ2822222-2-22-200002-2222002-2-22-20000-2-2-2-2-20000−2i2i00000000−2i−2i2i2i220000000000000000002i−2i0000
χ292222-2-22222222-2-2222-2-2-2-22-222222-20000000000000000-2-200000000000000000000002i−2i002i−2i00
χ302222-2-22222222-2-2222-2-2-2-22-222222-20000000000000000-2-20000000000000000000000−2i2i00−2i2i00
χ312222-2-2222-2-2-2-2-2-222222-2-22-22-2-2-2-2-200000000000000002200000000000000000000002i−2i00−2i2i00
χ322222-2-2222-2-2-2-2-2-222222-2-22-22-2-2-2-2-20000000000000000220000000000000000000000−2i2i002i−2i00
χ3322-2-22-2-2222i2i−2i−2i-222-2-22i−2i2-2-2-222i2i−2i−2i20000020-200002i−2i002i−2i0000000000020-2002i−2i000000000000
χ3422-2-22-2-2222i2i−2i−2i-222-2-22i−2i2-2-2-222i2i−2i−2i200000-2020000−2i2i002i−2i00000000000-20200−2i2i000000000000
χ3522-2-22-2-222−2i−2i2i2i-222-2-2−2i2i2-2-2-22−2i−2i2i2i20000020-20000−2i2i00−2i2i0000000000020-200−2i2i000000000000
χ3622-2-22-2-222−2i−2i2i2i-222-2-2−2i2i2-2-2-22−2i−2i2i2i200000-20200002i−2i00−2i2i00000000000-202002i−2i000000000000
χ3722-2-22-2-2-122i2i−2i−2i-22-1112i−2i-1111-1−i−iii-10000020-200−i3i32i−2i−i3i3−ii3−33−30000000-1013−3−ii−i3i30000000000
χ3822-2-22-2-2-122i2i−2i−2i-22-1112i−2i-1111-1−i−iii-10000020-200i3−i32i−2ii3−i3−ii−33−330000000-101−33−iii3−i30000000000
χ3922-2-22-2-2-122i2i−2i−2i-22-1112i−2i-1111-1−i−iii-100000-20200−i3i3−2i2i−i3i3−ii3−33−3000000010-1−33i−ii3−i30000000000
χ4022-2-22-2-2-122i2i−2i−2i-22-1112i−2i-1111-1−i−iii-100000-20200i3−i3−2i2ii3−i3−ii−33−33000000010-13−3i−i−i3i30000000000
χ4122-2-22-2-2-12−2i−2i2i2i-22-111−2i2i-1111-1ii−i−i-10000020-200−i3i3−2i2i−i3i3i−i−33−330000000-101−33i−i−i3i30000000000
χ4222-2-22-2-2-12−2i−2i2i2i-22-111−2i2i-1111-1ii−i−i-10000020-200i3−i3−2i2ii3−i3i−i3−33−30000000-1013−3i−ii3−i30000000000
χ4322-2-22-2-2-12−2i−2i2i2i-22-111−2i2i-1111-1ii−i−i-100000-20200−i3i32i−2i−i3i3i−i−33−33000000010-13−3−iii3−i30000000000
χ4422-2-22-2-2-12−2i−2i2i2i-22-111−2i2i-1111-1ii−i−i-100000-20200i3−i32i−2ii3−i3i−i3−33−3000000010-1−33−ii−i3i30000000000
χ4522-2-2-22-2222i2i−2i−2i2-22-2-2−2i2i-22-2222i2i−2i−2i-222-2-2000000000000−2i2i00002-22i2i−2i−2i00000000000000000000
χ4622-2-2-22-2222i2i−2i−2i2-22-2-2−2i2i-22-2222i2i−2i−2i-2-2-222000000000000−2i2i0000-22−2i−2i2i2i00000000000000000000
χ4722-2-2-22-222−2i−2i2i2i2-22-2-22i−2i-22-222−2i−2i2i2i-222-2-20000000000002i−2i00002-2−2i−2i2i2i00000000000000000000
χ4822-2-2-22-222−2i−2i2i2i2-22-2-22i−2i-22-222−2i−2i2i2i-2-2-2220000000000002i−2i0000-222i2i−2i−2i00000000000000000000
χ4922-2-2-2-222-20000222-2-200-2-222-20000222-2-220-20002200-2-2000000-22000000000000002-200000000
χ5022-2-2-2-222-20000222-2-200-2-222-20000222-2-2-202000-2-20022000000-2200000000000000-2200000000
χ5122-2-2-2-222-20000222-2-200-2-222-200002-2-22220-20002200-2-20000002-200000000000000-2200000000
χ5222-2-2-2-222-20000222-2-200-2-222-200002-2-222-202000-2-200220000002-2000000000000002-200000000
χ5344444-4-4-2-400004-4-2-2-200-222-2200002000000004i−4i00000000−2i−2i2i2i00000000000000000000000000
χ5444444-4-4-2-400004-4-2-2-200-222-220000200000000−4i4i000000002i2i−2i−2i00000000000000000000000000
χ554444-44-44-40000-4444400-44-4-4-400004000000000000000000000000000000000000000000000000
χ564444-44-4-2-40000-44-2-2-2002-22220000-20000000000−2i32i3002i3−2i300000000000000000000000000000000
χ574444-44-4-2-40000-44-2-2-2002-22220000-200000000002i3−2i300−2i32i300000000000000000000000000000000
χ584444-4-44-244444-4-4-2-2-2-4-422-22-2-2-2-2-22000000000000000022000000000000000000000000000000
χ594444-4-44-24-4-4-4-4-4-4-2-2-24422-22-2222220000000000000000-2-2000000000000000000000000000000
χ6044-4-44444-40000-4-44-4-400444-4-40000-4000000000000000000000000000000000000000000000000
χ6144-4-4444-2-40000-4-4-22200-2-2-22200002000000000000000000−2i32i32i3−2i300000000000000000000000000
χ6244-4-4444-2-40000-4-4-22200-2-2-222000020000000000000000002i3−2i3−2i32i300000000000000000000000000
χ6344-4-4-44-4-244i4i−4i−4i4-4-222−4i4i2-22-2-2−2i−2i2i2i200000000000000002i−2i000000000000000000000000000000
χ6444-4-4-44-4-24−4i−4i4i4i4-4-2224i−4i2-22-2-22i2i−2i−2i20000000000000000−2i2i000000000000000000000000000000
χ6544-4-4-4-44-2-4000044-2220022-2-220000-2000040-4000-2-2002200000000000000000000000000000000
χ6644-4-4-4-44-2-4000044-2220022-2-220000-20000-4040002200-2-200000000000000000000000000000000
χ674-44i−4i000402+2i−2−2i2−2i−2+2i00-44i−4i00000002+2i−2−2i2−2i−2+2i022−22−2i22i2000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ684-44i−4i000402+2i−2−2i2−2i−2+2i00-44i−4i00000002+2i−2−2i2−2i−2+2i0−22222i2−2i200000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ694-44i−4i00040−2−2i2+2i−2+2i2−2i00-44i−4i0000000−2−2i2+2i−2+2i2−2i022−22−2i22i200000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ704-44i−4i00040−2−2i2+2i−2+2i2−2i00-44i−4i0000000−2−2i2+2i−2+2i2−2i0−22222i2−2i2000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ714-4−4i4i000402−2i−2+2i2+2i−2−2i00-4−4i4i00000002−2i−2+2i2+2i−2−2i022−222i2−2i200000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ724-4−4i4i000402−2i−2+2i2+2i−2−2i00-4−4i4i00000002−2i−2+2i2+2i−2−2i0−2222−2i22i2000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ734-4−4i4i00040−2+2i2−2i−2−2i2+2i00-4−4i4i0000000−2+2i2−2i−2−2i2+2i022−222i2−2i2000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ744-4−4i4i00040−2+2i2−2i−2−2i2+2i00-4−4i4i0000000−2+2i2−2i−2−2i2+2i0−2222−2i22i200000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ758-88i−8i000-404+4i−4−4i4−4i−4+4i004−4i4i0000000−2−2i2+2i−2+2i2−2i0000000000000000000000000000000000000000000000000
χ768-88i−8i000-40−4−4i4+4i−4+4i4−4i004−4i4i00000002+2i−2−2i2−2i−2+2i0000000000000000000000000000000000000000000000000
χ778-8−8i8i000-404−4i−4+4i4+4i−4−4i0044i−4i0000000−2+2i2−2i−2−2i2+2i0000000000000000000000000000000000000000000000000
χ788-8−8i8i000-40−4+4i4−4i−4−4i4+4i0044i−4i00000002−2i−2+2i2+2i−2−2i0000000000000000000000000000000000000000000000000

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