Finite Group Databasebeta

← Group #10711296

Character table — Group #10711296

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444466668888888888888888881212121212121616161616161616161624242424242424244848
order124422234446888812126668812121224242424888822441616161624244848484848484848444488668812122424242488881616161688
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1
χ911-1-1-1-1111-11111-1-1-1-11-1-11-111-111-1-111-1-11-11-1ii−i−i1-1iiii−i−i−i−i11-1-11-11-1i−i1-1ii−i−i11-1-1ii−i−ii−i
χ1011-1-1-1-1111-11111-1-1-1-11-1-11-111-111-1-111-1-11-11-1−i−iii1-1−i−i−i−iiiii11-1-11-11-1−ii1-1−i−iii11-1-1−i−iii−ii
χ1111-1-1-1-1111-11111-1-1-1-11-1-11-111-111-1-111-1-1-11-11ii−i−i1-1iiii−i−i−i−i11-1-11-1-11−ii-11−i−iii-1-111ii−i−i−ii
χ1211-1-1-1-1111-11111-1-1-1-11-1-11-111-111-1-111-1-1-11-11−i−iii1-1−i−i−i−iiiii11-1-11-1-11i−i-11ii−i−i-1-111−i−iiii−i
χ1311-1-1-1-1111-11111-1-1-1-11-1-11-111-111-1-1-1-1111-11-1ii−i−i1-1iiii−i−i−i−i-1-111-111-1i−i1-1ii−i−i-1-111−i−iii−ii
χ1411-1-1-1-1111-11111-1-1-1-11-1-11-111-111-1-1-1-1111-11-1−i−iii1-1−i−i−i−iiiii-1-111-111-1−ii1-1−i−iii-1-111ii−i−ii−i
χ1511-1-1-1-1111-11111-1-1-1-11-1-11-111-111-1-1-1-111-11-11ii−i−i1-1iiii−i−i−i−i-1-111-11-11−ii-11−i−iii11-1-1−i−iiii−i
χ1611-1-1-1-1111-11111-1-1-1-11-1-11-111-111-1-1-1-111-11-11−i−iii1-1−i−i−i−iiiii-1-111-11-11i−i-11ii−i−i11-1-1ii−i−i−ii
χ17222222222222-2-2-2-222222-2-2222-2-2-2-2222200000000-2-200000000-2-2-2-22200000000000000000000
χ18222222222222-2-2-2-222222-2-2222-2-2-2-2-2-2-2-200000000-2-2000000002222-2-200000000000000000000
χ192222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-1000022222222-1-1-1-1-1-1-1-1-1-1000000-1-122-1-1-1-1-1-10000000000
χ202222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-100002222-2-2-2-2-1-111111111000000-1-1-2-2-1-111110000000000
χ212222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-10000-2-2-2-22222-1-1-1-1-1-1-1-1-1-100000011-2-21111110000000000
χ222222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-1-111111111000000112211-1-1-1-10000000000
χ2322222-2-222-2-22222222-22-2-2-2-22-22222000000000000-2-20000000000000000000000002i−2i2i−2i000000
χ2422222-2-222-2-22222222-22-2-2-2-22-22222000000000000-2-2000000000000000000000000−2i2i−2i2i000000
χ2522222-2-222-2-22-2-2-2-222-22-222-22-2-2-2-2-200002-2-22000022000000000000002-200-2200000000000000
χ2622222-2-222-2-22-2-2-2-222-22-222-22-2-2-2-2-20000-222-200002200000000000000-22002-200000000000000
χ2722222-2-2-12-2-2-1-2-2-2-2-1-11-11221-11111100002-2-220000-1-133−3−333−3−3000000-11001-13−33−30000000000
χ2822222-2-2-12-2-2-1-2-2-2-2-1-11-11221-11111100002-2-220000-1-1−3−333−3−333000000-11001-1−33−330000000000
χ2922222-2-2-12-2-2-1-2-2-2-2-1-11-11221-1111110000-222-20000-1-133−3−333−3−30000001-100-11−33−330000000000
χ3022222-2-2-12-2-2-1-2-2-2-2-1-11-11221-1111110000-222-20000-1-1−3−333−3−3330000001-100-113−33−30000000000
χ312222-22-22-2-222000022-2-22002-2-2000022220000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i20000-2-200000000000000−i2i2−i2i200
χ322222-22-22-2-222000022-2-22002-2-2000022220000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i20000-2-200000000000000i2−i2i2−i200
χ332222-22-22-2-222000022-2-22002-2-20000-2-2-2-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i200002200000000000000i2−i2i2−i200
χ342222-22-22-2-222000022-2-22002-2-20000-2-2-2-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i200002200000000000000−i2i2−i2i200
χ3522-2-22-2-22-22220000-2-2-22-2002-22000022-2-200002−2−22002−22−2−22−220000-22000000000000002−2−2200
χ3622-2-22-2-22-22220000-2-2-22-2002-22000022-2-20000−222−200−22−222−22−20000-2200000000000000−222−200
χ3722-2-22-2-22-22220000-2-2-22-2002-220000-2-22200002−2−22002−22−2−22−2200002-200000000000000−222−200
χ3822-2-22-2-22-22220000-2-2-22-2002-220000-2-2220000−222−200−22−222−22−200002-2000000000000002−2−2200
χ3922-2-2-22-2222-2222-2-2-2-2-2-22-22-22222-2-2000000000000-220000000000000000000000002i−2i−2i2i000000
χ4022-2-2-22-2222-2222-2-2-2-2-2-22-22-22222-2-2000000000000-22000000000000000000000000−2i2i2i−2i000000
χ4122-2-2-22-2222-22-2-222-2-2-2-222-2-222-2-222000022-2-200002-2000000000000002200-2-200000000000000
χ4222-2-2-22-2222-22-2-222-2-2-2-222-2-222-2-2220000-2-22200002-200000000000000-2-2002200000000000000
χ4322-2-2-22-2-122-2-1-2-2221111-12-21-1-111-1-1000022-2-20000-11−i3−i3i3i3i3i3−i3−i3000000-1-10011−i3i3i3−i30000000000
χ4422-2-2-22-2-122-2-1-2-2221111-12-21-1-111-1-1000022-2-20000-11i3i3−i3−i3−i3−i3i3i3000000-1-10011i3−i3−i3i30000000000
χ4522-2-2-22-2-122-2-1-2-2221111-12-21-1-111-1-10000-2-2220000-11−i3−i3i3i3i3i3−i3−i30000001100-1-1i3−i3−i3i30000000000
χ4622-2-2-22-2-122-2-1-2-2221111-12-21-1-111-1-10000-2-2220000-11i3i3−i3−i3−i3−i3i3i30000001100-1-1−i3i3i3−i30000000000
χ4722-2-2-2-2222-222-2-222-2-22-2-2-2222-2-2-22222-2-200000000-2200000000-2-2222-200000000000000000000
χ4822-2-2-2-2222-222-2-222-2-22-2-2-2222-2-2-222-2-22200000000-220000000022-2-2-2200000000000000000000
χ4922-2-2-2-22-12-22-122-2-211-1112-2-1-11-1-11100002-22-22i2i−2i−2i-11−i−i−i−iiiii000000-112i−2i-11−i−iii0000000000
χ5022-2-2-2-22-12-22-122-2-211-1112-2-1-11-1-11100002-22-2−2i−2i2i2i-11iiii−i−i−i−i000000-11−2i2i-11ii−i−i0000000000
χ5122-2-2-2-22-12-22-122-2-211-1112-2-1-11-1-1110000-22-222i2i−2i−2i-11−i−i−i−iiiii0000001-1−2i2i1-1ii−i−i0000000000
χ5222-2-2-2-22-12-22-122-2-211-1112-2-1-11-1-1110000-22-22−2i−2i2i2i-11iiii−i−i−i−i0000001-12i−2i1-1−i−iii0000000000
χ534444444-2444-2-4-4-4-4-2-2-2-2-2-4-4-2-2-22222000000000000220000000000000000000000000000000000
χ5444444-4-4-24-4-4-24444-2-22-22-4-42-22-2-2-2-2000000000000220000000000000000000000000000000000
χ554444-44-4-2-4-44-20000-2-222-200-222000000000000−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ564444-44-4-2-4-44-20000-2-222-200-2220000000000002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ574444-4-444-44-440000444-4-400-4-440000000000000000000000000000000000000000000000000000
χ584444-4-44-2-44-4-20000-2-2-2220022-2000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ594444-4-44-2-44-4-20000-2-2-2220022-2000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ6044-4-44444-4-4-440000-4-444400-4-4-40000000000000000000000000000000000000000000000000000
χ6144-4-4444-2-4-4-4-2000022-2-2-2002220000000000000000006−6−66−666−600000000000000000000000000
χ6244-4-4444-2-4-4-4-2000022-2-2-200222000000000000000000−666−66−6−6600000000000000000000000000
χ6344-4-44-4-4-2-444-20000222-2200-22-200000000000022−22−222200−22−222−22−200000000000000000000000000
χ6444-4-44-4-4-2-444-20000222-2200-22-2000000000000−222222−22002−22−2−22−2200000000000000000000000000
χ6544-4-4-44-4-244-4-244-4-42222-2-442-2-2-2-2220000000000002-20000000000000000000000000000000000
χ6644-4-4-4-44-24-44-2-4-44422-222-44-2-2222-2-20000000000002-20000000000000000000000000000000000
χ674-44i−4i0004000-4−2i22i222−224i−4i00000000−2i22i222−2222−22−2i22i20000000000000000002i−2i2-20000000000000000000000
χ684-44i−4i0004000-4−2i22i222−224i−4i00000000−2i22i222−22−22222i2−2i2000000000000000000−2i2i-220000000000000000000000
χ694-44i−4i0004000-42i2−2i2−22224i−4i000000002i2−2i2−222222−22−2i22i2000000000000000000−2i2i-220000000000000000000000
χ704-44i−4i0004000-42i2−2i2−22224i−4i000000002i2−2i2−2222−22222i2−2i20000000000000000002i−2i2-20000000000000000000000
χ714-4−4i4i0004000-4−2i22i2−2222−4i4i00000000−2i22i2−222222−222i2−2i20000000000000000002i−2i-220000000000000000000000
χ724-4−4i4i0004000-4−2i22i2−2222−4i4i00000000−2i22i2−2222−2222−2i22i2000000000000000000−2i2i2-20000000000000000000000
χ734-4−4i4i0004000-42i2−2i222−22−4i4i000000002i2−2i222−2222−222i2−2i2000000000000000000−2i2i2-20000000000000000000000
χ744-4−4i4i0004000-42i2−2i222−22−4i4i000000002i2−2i222−22−2222−2i22i20000000000000000002i−2i-220000000000000000000000
χ758-88i−8i000-40004−4i24i242−42−4i4i000000002i2−2i2−2222000000000000000000000000000000000000000000000000
χ768-88i−8i000-400044i2−4i2−4242−4i4i00000000−2i22i222−22000000000000000000000000000000000000000000000000
χ778-8−8i8i000-40004−4i24i2−42424i−4i000000002i2−2i222−22000000000000000000000000000000000000000000000000
χ788-8−8i8i000-400044i2−4i242−424i−4i00000000−2i22i2−2222000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).