Finite Group Databasebeta

← Group #70951

Character table — Group #70951

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222222222222444444444444666666666666666688888888888824242424
order122244443444466688888888121212121212121224242424242424248888888888888888448812121212242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111-1-1-1-1111-1-1111ii−i−iii−i−i-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-1i−i
χ101111-1-1-1-1111-1-1111ii−i−iii−i−i-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-11−ii
χ111111-1-1-1-1111-1-1111ii−i−iii−i−i-1-1-1-111-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii1-1i−i11-1-1ii−i−i-11−ii
χ121111-1-1-1-1111-1-1111ii−i−iii−i−i-1-1-1-111-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii-11−ii-1-111−i−iii1-1i−i
χ131111-1-1-1-1111-1-1111−i−iii−i−iii-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1-1−ii
χ141111-1-1-1-1111-1-1111−i−iii−i−iii-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-11i−i
χ151111-1-1-1-1111-1-1111−i−iii−i−iii-1-1-1-111-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i1-1−ii11-1-1−i−iii-11i−i
χ161111-1-1-1-1111-1-1111−i−iii−i−iii-1-1-1-111-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i-11i−i-1-111ii−i−i1-1−ii
χ17222222222-2-2-2-22222222-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ18222222222-2-2-2-2222-2-2-2-222222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ1922222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ2022222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ2122222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ2222222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ2322222222-1-2-2-2-2-1-1-12222-2-2-2-2-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2422222222-1-2-2-2-2-1-1-12222-2-2-2-2-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2522222222-1-2-2-2-2-1-1-1-2-2-2-22222-1-1-1-111111111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ2622222222-1-2-2-2-2-1-1-1-2-2-2-22222-1-1-1-111111111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ272222-2-2-2-22-2-2222222i2i−2i−2i−2i−2i2i2i-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ282222-2-2-2-22-2-222222−2i−2i2i2i2i2i−2i−2i-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ292222-2-2-2-2-122-2-2-1-1-12i2i−2i−2i2i2i−2i−2i1111-1-111−i−iii−i−iii00000000000000002-22i−2i-1-111−i−iii0000
χ302222-2-2-2-2-122-2-2-1-1-12i2i−2i−2i2i2i−2i−2i1111-1-111−i−iii−i−iii0000000000000000-22−2i2i11-1-1ii−i−i0000
χ312222-2-2-2-2-122-2-2-1-1-1−2i−2i2i2i−2i−2i2i2i1111-1-111ii−i−iii−i−i00000000000000002-2−2i2i-1-111ii−i−i0000
χ322222-2-2-2-2-122-2-2-1-1-1−2i−2i2i2i−2i−2i2i2i1111-1-111ii−i−iii−i−i0000000000000000-222i−2i11-1-1−i−iii0000
χ332222-2-2-2-2-1-2-222-1-1-12i2i−2i−2i−2i−2i2i2i111111-1-1−i−iiiii−i−i00000000000000000000−i3i3i3−i33−3−330000
χ342222-2-2-2-2-1-2-222-1-1-12i2i−2i−2i−2i−2i2i2i111111-1-1−i−iiiii−i−i00000000000000000000i3−i3−i3i3−333−30000
χ352222-2-2-2-2-1-2-222-1-1-1−2i−2i2i2i2i2i−2i−2i111111-1-1ii−i−i−i−iii00000000000000000000−i3i3i3−i3−333−30000
χ362222-2-2-2-2-1-2-222-1-1-1−2i−2i2i2i2i2i−2i−2i111111-1-1ii−i−i−i−iii00000000000000000000i3−i3−i3i33−3−330000
χ3722-2-222-2-2200002-2-22-22-2000022-2-200002-22-2000022−2−222−2−222−2−222−2−20000000000000000
χ3822-2-222-2-2200002-2-22-22-2000022-2-200002-22-20000−2−222−2−222−2−222−2−2220000000000000000
χ3922-2-222-2-2200002-2-2-22-22000022-2-20000-22-22000022−2−222−2−2−2−222−2−2220000000000000000
χ4022-2-222-2-2200002-2-2-22-22000022-2-20000-22-220000−2−222−2−22222−2−222−2−20000000000000000
χ4122-2-2-2-222200002-2-22i−2i−2i2i0000-2-22200002i−2i−2i2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ4222-2-2-2-222200002-2-22i−2i−2i2i0000-2-22200002i−2i−2i2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ4322-2-2-2-222200002-2-2−2i2i2i−2i0000-2-2220000−2i2i2i−2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ4422-2-2-2-222200002-2-2−2i2i2i−2i0000-2-2220000−2i2i2i−2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ452-22-22i−2i2i−2i20000-22-20000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232i−2i2i−2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232−22−2−i2i2−i2i21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ462-22-22i−2i2i−2i20000-22-20000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232i−2i2i−2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−22−22i2−i2i2−i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ472-22-22i−2i2i−2i20000-22-200002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232i−2i2i−2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232−22−2−i2i2−i2i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ482-22-22i−2i2i−2i20000-22-200002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232i−2i2i−2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−22−22i2−i2i2−i21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ492-22-2−2i2i−2i2i20000-22-200002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2i2i−2i2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132−22−2i2−i2i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ502-22-2−2i2i−2i2i20000-22-200002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2i2i−2i2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−22−22−i2i2−i2i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ512-22-2−2i2i−2i2i20000-22-20000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2i2i−2i2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132−22−2i2−i2i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ522-22-2−2i2i−2i2i20000-22-20000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2i2i−2i2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−22−22−i2i2−i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ532-2-222i−2i−2i2i22-22i−2i-2-22000000002i−2i−2i2i2-22i−2i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ542-2-222i−2i−2i2i22-22i−2i-2-22000000002i−2i−2i2i2-22i−2i00000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ552-2-222i−2i−2i2i2-22−2i2i-2-22000000002i−2i−2i2i-22−2i2i000000002-2-22−2i2i2i−2i000000000000000000000000
χ562-2-222i−2i−2i2i2-22−2i2i-2-22000000002i−2i−2i2i-22−2i2i00000000-222-22i−2i−2i2i000000000000000000000000
χ572-2-22−2i2i2i−2i22-2−2i2i-2-2200000000−2i2i2i−2i2-2−2i2i00000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ582-2-22−2i2i2i−2i22-2−2i2i-2-2200000000−2i2i2i−2i2-2−2i2i0000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ592-2-22−2i2i2i−2i2-222i−2i-2-2200000000−2i2i2i−2i-222i−2i000000002-2-222i−2i−2i2i000000000000000000000000
χ602-2-22−2i2i2i−2i2-222i−2i-2-2200000000−2i2i2i−2i-222i−2i00000000-222-2−2i2i2i−2i000000000000000000000000
χ6144-4-444-4-4-20000-2224-44-40000-2-2220000-22-22000000000000000000000000000000000000
χ6244-4-444-4-4-20000-222-44-440000-2-22200002-22-2000000000000000000000000000000000000
χ6344-4-4-4-444-20000-2224i−4i−4i4i000022-2-20000−2i2i2i−2i000000000000000000000000000000000000
χ6444-4-4-4-444-20000-222−4i4i4i−4i000022-2-200002i−2i−2i2i000000000000000000000000000000000000
χ654-44-44i−4i4i−4i-200002-220000−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ23−2i2i−2i2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000
χ664-44-44i−4i4i−4i-200002-2200004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ23−2i2i−2i2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000
χ674-44-4−4i4i−4i4i-200002-2200004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ132i−2i2i−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ684-44-4−4i4i−4i4i-200002-220000−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ132i−2i2i−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000000000
χ694-4-444i−4i−4i4i-24-44i−4i22-200000000−2i2i2i−2i-22−2i2i0000000000000000000000000000000000000000
χ704-4-444i−4i−4i4i-2-44−4i4i22-200000000−2i2i2i−2i2-22i−2i0000000000000000000000000000000000000000
χ714-4-44−4i4i4i−4i-24-4−4i4i22-2000000002i−2i−2i2i-222i−2i0000000000000000000000000000000000000000
χ724-4-44−4i4i4i−4i-2-444i−4i22-2000000002i−2i−2i2i2-2−2i2i0000000000000000000000000000000000000000

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