Finite Group Databasebeta

← Group #10877374

Character table — Group #10877374

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222224444444444444466668888888888888888888888121212121212161616161616161624242424242424244848
order1244222344461212224466688881212128888668888881212242424242424242424242424444488441212121224242488888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ5111111111111111111111-1-1-1-11111111111111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ6111111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ7111111111111111111111-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1111111-1-1-1-1
χ911111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-11111111-111-1-1-1-1-1-111-1-1-1-11-1
χ1011111111111111-1-1-1-111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111111111-11-1-111-1-1-1-1-1-111-1-1-11
χ1111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-11111-11
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11-1-111-1-11111-1-1111-1
χ1311111111111111-1-1-1-1111-1-1-1-11111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-11-1-111111111-1-1-1-1-11
χ1411111111111111-1-1-1-1111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-111-1-11111-1-111-1-11-1
χ1511111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-11-1-11111-1-1-1-111111-1
χ1611111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-11-111-1-111-1-111-1-111-11
χ172222222-1222-1-1-12222-1-1-12222-1-1-10000-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-10000000000
χ182222222-1222-1-1-12222-1-1-12222-1-1-10000-1-1-2-2-2-222-1-1-1-1-1-111111111000000-2-21111-1-10000000000
χ192222222-1222-1-1-12222-1-1-1-2-2-2-2-1-1-10000-1-12222-2-2-1-11111-1-1-1-1-1-1-1-1000000-2-21111110000000000
χ202222222-1222-1-1-12222-1-1-1-2-2-2-2-1-1-10000-1-1-2-2-2-2-2-2-1-111111111111100000022-1-1-1-1110000000000
χ212222222-1222-1-1-1-2-2-2-2-1-1-12222-1-1-100001122-2-2-2-211-1-1-1-1-1-1-1-111110000002-2-1-111110000000000
χ222222222-1222-1-1-1-2-2-2-2-1-1-12222-1-1-1000011-2-222-2-211-1-1-1-11111-1-1-1-1000000-2211-1-1110000000000
χ232222222-1222-1-1-1-2-2-2-2-1-1-1-2-2-2-2-1-1-100001122-2-222111111-1-1-1-11111000000-2211-1-1-1-10000000000
χ242222222-1222-1-1-1-2-2-2-2-1-1-1-2-2-2-2-1-1-1000011-2-222221111111111-1-1-1-10000002-2-1-111-1-10000000000
χ2522222-2-22-2-222222-22-22-2-20000-2-2222222-20000002-20000000000000000-2-2000000000000002-200
χ2622222-2-22-2-222222-22-22-2-20000-2-22-2-2-2-22-20000002-200000000000000002200000000000000-2200
χ2722222-2-22-2-22222-22-222-2-20000-2-222222-22000000-220000000000000000-2-200000000000000-2200
χ2822222-2-22-2-22222-22-222-2-20000-2-22-2-2-2-2-22000000-22000000000000000022000000000000002-200
χ2922-2-22222-2-2-22-2-22-2-222222i2i−2i−2i-2-2-200002-200002i−2i-222i2i−2i−2i000000000000000000002i−2i0000000000
χ3022-2-22222-2-2-22-2-22-2-22222−2i−2i2i2i-2-2-200002-20000−2i2i-22−2i−2i2i2i00000000000000000000−2i2i0000000000
χ3122-2-22222-2-2-22-2-2-222-22222i2i−2i−2i-2-2-20000-220000−2i2i2-22i2i−2i−2i00000000000000000000−2i2i0000000000
χ3222-2-22222-2-2-22-2-2-222-2222−2i−2i2i2i-2-2-20000-2200002i−2i2-2−2i−2i2i2i000000000000000000002i−2i0000000000
χ3322-2-2222-1-2-2-2-1112-2-22-1-1-12i2i−2i−2i1110000-1100002i−2i1-1−i−iii33−3−333−3−300000000−i3i3−i3i3−ii0000000000
χ3422-2-2222-1-2-2-2-1112-2-22-1-1-12i2i−2i−2i1110000-1100002i−2i1-1−i−iii−3−333−3−33300000000i3−i3i3−i3−ii0000000000
χ3522-2-2222-1-2-2-2-1112-2-22-1-1-1−2i−2i2i2i1110000-110000−2i2i1-1ii−i−i33−3−333−3−300000000i3−i3i3−i3i−i0000000000
χ3622-2-2222-1-2-2-2-1112-2-22-1-1-1−2i−2i2i2i1110000-110000−2i2i1-1ii−i−i−3−333−3−33300000000−i3i3−i3i3i−i0000000000
χ3722-2-2222-1-2-2-2-111-222-2-1-1-12i2i−2i−2i11100001-10000−2i2i-11−i−iii33−3−3−3−33300000000−i3i3i3−i3i−i0000000000
χ3822-2-2222-1-2-2-2-111-222-2-1-1-12i2i−2i−2i11100001-10000−2i2i-11−i−iii−3−33333−3−300000000i3−i3−i3i3i−i0000000000
χ3922-2-2222-1-2-2-2-111-222-2-1-1-1−2i−2i2i2i11100001-100002i−2i-11ii−i−i33−3−3−3−33300000000i3−i3−i3i3−ii0000000000
χ4022-2-2222-1-2-2-2-111-222-2-1-1-1−2i−2i2i2i11100001-100002i−2i-11ii−i−i−3−33333−3−300000000−i3i3i3−i3−ii0000000000
χ4122-2-22-2-2222-22-2-222-2-22-2-2000022-2000022000000-2-200000000000022-2-200000000002-200000000
χ4222-2-22-2-2222-22-2-222-2-22-2-2000022-2000022000000-2-2000000000000-2-2220000000000-2200000000
χ4322-2-22-2-2222-22-2-2-2-2222-2-2000022-20000-2-20000002200000000000022-2-20000000000-2200000000
χ4422-2-22-2-2222-22-2-2-2-2222-2-2000022-20000-2-200000022000000000000-2-22200000000002-200000000
χ4522-2-2-22-222-222-2-20000-22-200002-2222-2-200002i−2i0000000000002i−2i2i−2i00002-20000000000002i−2i0000
χ4622-2-2-22-222-222-2-20000-22-200002-2222-2-20000−2i2i000000000000−2i2i−2i2i00002-2000000000000−2i2i0000
χ4722-2-2-22-222-222-2-20000-22-200002-22-2-22200002i−2i0000000000002i−2i2i−2i0000-22000000000000−2i2i0000
χ4822-2-2-22-222-222-2-20000-22-200002-22-2-2220000−2i2i000000000000−2i2i−2i2i0000-220000000000002i−2i0000
χ4922-2-2-2-222-2222-2-20000-2-220000-22222-2-2002i−2i00000000002i−2i2i−2i00000000-2200000000002i−2i000000
χ5022-2-2-2-222-2222-2-20000-2-220000-22222-2-200−2i2i0000000000−2i2i−2i2i00000000-220000000000−2i2i000000
χ5122-2-2-2-222-2222-2-20000-2-220000-222-2-222002i−2i00000000002i−2i2i−2i000000002-20000000000−2i2i000000
χ5222-2-2-2-222-2222-2-20000-2-220000-222-2-22200−2i2i0000000000−2i2i−2i2i000000002-200000000002i−2i000000
χ5344444-4-4-2-4-44-2-2-24-44-4-222000022-20000-22000000-22000000000000000000000000000000000000
χ5444444-4-4-2-4-44-2-2-2-44-44-222000022-200002-20000002-2000000000000000000000000000000000000
χ554444-44-44-44-44440000-44-40000-44-400000000000000000000000000000000000000000000000000
χ564444-44-4-2-44-4-2-2-200002-2200002-220000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ574444-44-4-2-44-4-2-2-200002-2200002-2200000000000000000000002i3−2i3−2i32i3000000000000000000000000
χ584444-4-4444-4-44440000-4-4400004-4-400000000000000000000000000000000000000000000000000
χ594444-4-44-24-4-4-2-2-2000022-20000-222000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ604444-4-44-24-4-4-2-2-2000022-20000-2220000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ6144-4-44-4-4-244-4-22244-4-4-2220000-2-220000-2-200000022000000000000000000000000000000000000
χ6244-4-44-4-4-244-4-222-4-444-2220000-2-22000022000000-2-2000000000000000000000000000000000000
χ6344-4-4-44-4-24-44-22200002-220000-22-2000000004i−4i000000000000−2i2i−2i2i000000000000000000000000
χ6444-4-4-44-4-24-44-22200002-220000-22-200000000−4i4i0000000000002i−2i2i−2i000000000000000000000000
χ6544-4-4-4-44-2-444-222000022-200002-2-20000004i−4i0000000000−2i2i−2i2i0000000000000000000000000000
χ6644-4-4-4-44-2-444-222000022-200002-2-2000000−4i4i00000000002i−2i2i−2i0000000000000000000000000000
χ674-44i−4i0004000-44i−4i00000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300022−22−2i22i200000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000002-22i−2i00000000000000000000
χ684-44i−4i0004000-44i−4i00000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000−22222i2−2i200000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000-22−2i2i00000000000000000000
χ694-44i−4i0004000-44i−4i0000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300022−22−2i22i20000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000-22−2i2i00000000000000000000
χ704-44i−4i0004000-44i−4i0000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000−22222i2−2i20000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000002-22i−2i00000000000000000000
χ714-4−4i4i0004000-4−4i4i0000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300022−222i2−2i20000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000002-2−2i2i00000000000000000000
χ724-4−4i4i0004000-4−4i4i0000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000−2222−2i22i20000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000-222i−2i00000000000000000000
χ734-4−4i4i0004000-4−4i4i00000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300022−222i2−2i200000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000-222i−2i00000000000000000000
χ744-4−4i4i0004000-4−4i4i00000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000−2222−2i22i200000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000002-2−2i2i00000000000000000000
χ758-88i−8i000-40004−4i4i00000004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ1300000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ768-88i−8i000-40004−4i4i0000000−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ13000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000000000
χ778-8−8i8i000-400044i−4i0000000−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ23000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000
χ788-8−8i8i000-400044i−4i00000004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ2300000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000

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