Finite Group Databasebeta

← Group #68529

Character table — Group #68529

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222222222222444444444444666666666666666688888888888824242424
order122244443444466688888888121212121212121224242424242424242244444488888888888824242424242424248888
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
χ91111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−ii−ii−i
χ101111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−ii−ii
χ111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111i−ii−iii−i−iii−i−i−ii−ii
χ121111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111−ii−ii−i−iii−i−iiii−ii−i
χ131111-1-1-1-11-1-111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiii−i−ii
χ141111-1-1-1-11-1-111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−iii−i
χ151111-1-1-1-11-1-111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1i−i−iiii−i−i−i−iii−iii−i
χ161111-1-1-1-11-1-111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1−iii−i−i−iiiii−i−ii−i−ii
χ17222222222-2-2-2-2222000000002222-2-2-2-20000000022-2-222-2-2000000000000000000000000
χ18222222222-2-2-2-2222000000002222-2-2-2-200000000-2-222-2-222000000000000000000000000
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
χ232222-2-2-2-2222-2-222200000000-2-2-2-222-2-20000000022-2-2-2-222000000000000000000000000
χ242222-2-2-2-2222-2-222200000000-2-2-2-222-2-200000000-2-22222-2-2000000000000000000000000
χ252222-2-2-2-2-1-2-222-1-1-12222-2-2-2-2111111-1-1-1-1-1-1111100000000000000002i−2i2i−2i−i−iii−i−iii0000
χ262222-2-2-2-2-1-2-222-1-1-12222-2-2-2-2111111-1-1-1-1-1-111110000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ272222-2-2-2-2-1-2-222-1-1-1-2-2-2-22222111111-1-11111-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ282222-2-2-2-2-1-2-222-1-1-1-2-2-2-22222111111-1-11111-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ2922-2-222-2-2200002-2-2−i2−i2i2i2−i2−i2i2i222-2-20000−i2−i2i2i2−i2−i2i2i22-2002-200−i2−i2i2i2−i2−i2i2i20000000000000000
χ3022-2-222-2-2200002-2-2−i2−i2i2i2−i2−i2i2i222-2-20000−i2−i2i2i2−i2−i2i2i2-2200-2200i2i2−i2−i2i2i2−i2−i20000000000000000
χ3122-2-222-2-2200002-2-2i2i2−i2−i2i2i2−i2−i222-2-20000i2i2−i2−i2i2i2−i2−i22-2002-200i2i2−i2−i2i2i2−i2−i20000000000000000
χ3222-2-222-2-2200002-2-2i2i2−i2−i2i2i2−i2−i222-2-20000i2i2−i2−i2i2i2−i2−i2-2200-2200−i2−i2i2i2−i2−i2i2i20000000000000000
χ3322-2-2-2-222200002-2-2−i2−i2i2i2i2i2−i2−i2-2-2220000−i2−i2i2i2i2i2−i2−i22-200-2200−i2−i2i2i2i2i2−i2−i20000000000000000
χ3422-2-2-2-222200002-2-2−i2−i2i2i2i2i2−i2−i2-2-2220000−i2−i2i2i2i2i2−i2−i2-22002-200i2i2−i2−i2−i2−i2i2i20000000000000000
χ3522-2-2-2-222200002-2-2i2i2−i2−i2−i2−i2i2i2-2-2220000i2i2−i2−i2−i2−i2i2i22-200-2200i2i2−i2−i2−i2−i2i2i20000000000000000
χ3622-2-2-2-222200002-2-2i2i2−i2−i2−i2−i2i2i2-2-2220000i2i2−i2−i2−i2−i2i2i2-22002-200−i2−i2i2i2i2i2−i2−i20000000000000000
χ372-22-22i−2i2i−2i20000-22-22−22−2−i2i2−i2i22i−2i2i−2i00002−22−2−i2i2−i2i2002i−2i002-2−i2i2−i2i22−22−20000000000000000
χ382-22-22i−2i2i−2i20000-22-22−22−2−i2i2−i2i22i−2i2i−2i00002−22−2−i2i2−i2i200−2i2i00-22i2−i2i2−i2−22−220000000000000000
χ392-22-22i−2i2i−2i20000-22-2−22−22i2−i2i2−i22i−2i2i−2i0000−22−22i2−i2i2−i2002i−2i002-2i2−i2i2−i2−22−220000000000000000
χ402-22-22i−2i2i−2i20000-22-2−22−22i2−i2i2−i22i−2i2i−2i0000−22−22i2−i2i2−i200−2i2i00-22−i2i2−i2i22−22−20000000000000000
χ412-22-2−2i2i−2i2i20000-22-22−22−2i2−i2i2−i2−2i2i−2i2i00002−22−2i2−i2i2−i2002i−2i00-22−i2i2−i2i2−22−220000000000000000
χ422-22-2−2i2i−2i2i20000-22-22−22−2i2−i2i2−i2−2i2i−2i2i00002−22−2i2−i2i2−i200−2i2i002-2i2−i2i2−i22−22−20000000000000000
χ432-22-2−2i2i−2i2i20000-22-2−22−22−i2i2−i2i2−2i2i−2i2i0000−22−22−i2i2−i2i2002i−2i00-22i2−i2i2−i22−22−20000000000000000
χ442-22-2−2i2i−2i2i20000-22-2−22−22−i2i2−i2i2−2i2i−2i2i0000−22−22−i2i2−i2i200−2i2i002-2−i2i2−i2i2−22−220000000000000000
χ452-2-222i−2i−2i2i22i−2i2-2-2-22000000002i−2i−2i2i2i−2i2-200000000000000002-2-222i−2i−2i2i0000000000000000
χ462-2-222i−2i−2i2i22i−2i2-2-2-22000000002i−2i−2i2i2i−2i2-20000000000000000-222-2−2i2i2i−2i0000000000000000
χ472-2-222i−2i−2i2i2−2i2i-22-2-222i−2i−2i2i2-2-222i−2i−2i2i−2i2i-222i−2i−2i2i2-2-2200000000000000000000000000000000
χ482-2-222i−2i−2i2i2−2i2i-22-2-22−2i2i2i−2i-222-22i−2i−2i2i−2i2i-22−2i2i2i−2i-222-200000000000000000000000000000000
χ492-2-222i−2i−2i2i-1−2i2i-2211-12i−2i−2i2i2-2-22−iii−ii−i1-1−iii−i-111-100000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ502-2-222i−2i−2i2i-1−2i2i-2211-12i−2i−2i2i2-2-22−iii−ii−i1-1−iii−i-111-100000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ512-2-222i−2i−2i2i-1−2i2i-2211-1−2i2i2i−2i-222-2−iii−ii−i1-1i−i−ii1-1-1100000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ522-2-222i−2i−2i2i-1−2i2i-2211-1−2i2i2i−2i-222-2−iii−ii−i1-1i−i−ii1-1-1100000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ532-2-22−2i2i2i−2i22i−2i-22-2-222i−2i−2i2i-222-2−2i2i2i−2i2i−2i-222i−2i−2i2i-222-200000000000000000000000000000000
χ542-2-22−2i2i2i−2i22i−2i-22-2-22−2i2i2i−2i2-2-22−2i2i2i−2i2i−2i-22−2i2i2i−2i2-2-2200000000000000000000000000000000
χ552-2-22−2i2i2i−2i2−2i2i2-2-2-2200000000−2i2i2i−2i−2i2i2-200000000000000002-2-22−2i2i2i−2i0000000000000000
χ562-2-22−2i2i2i−2i2−2i2i2-2-2-2200000000−2i2i2i−2i−2i2i2-20000000000000000-222-22i−2i−2i2i0000000000000000
χ572-2-22−2i2i2i−2i-12i−2i-2211-12i−2i−2i2i-222-2i−i−ii−ii1-1−iii−i1-1-1100000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000
χ582-2-22−2i2i2i−2i-12i−2i-2211-12i−2i−2i2i-222-2i−i−ii−ii1-1−iii−i1-1-1100000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ592-2-22−2i2i2i−2i-12i−2i-2211-1−2i2i2i−2i2-2-22i−i−ii−ii1-1i−i−ii-111-100000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ602-2-22−2i2i2i−2i-12i−2i-2211-1−2i2i2i−2i2-2-22i−i−ii−ii1-1i−i−ii-111-100000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000
χ6144444444-2-4-4-4-4-2-2-200000000-2-2-2-222220000000000000000000000000000000000000000
χ624444-4-4-4-4-244-4-4-2-2-2000000002222-2-2220000000000000000000000000000000000000000
χ6344-4-444-4-4-20000-222−2i2−2i22i22i2−2i2−2i22i22i2-2-2220000i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ6444-4-444-4-4-20000-2222i22i2−2i2−2i22i22i2−2i2−2i2-2-2220000−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ6544-4-4-4-444-20000-222−2i2−2i22i22i22i22i2−2i2−2i222-2-20000i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ6644-4-4-4-444-20000-2222i22i2−2i2−2i2−2i2−2i22i22i222-2-20000−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ674-44-44i−4i4i−4i-200002-2222−2222−22−2i22i2−2i22i2−2i2i−2i2i0000−22−22i2−i2i2−i200000000000000000000000000000000
χ684-44-44i−4i4i−4i-200002-22−2222−22222i2−2i22i2−2i2−2i2i−2i2i00002−22−2−i2i2−i2i200000000000000000000000000000000
χ694-44-4−4i4i−4i4i-200002-2222−2222−222i2−2i22i2−2i22i−2i2i−2i0000−22−22−i2i2−i2i200000000000000000000000000000000
χ704-44-4−4i4i−4i4i-200002-22−2222−2222−2i22i2−2i22i22i−2i2i−2i00002−22−2i2−i2i2−i200000000000000000000000000000000
χ714-4-444i−4i−4i4i-24i−4i4-422-200000000−2i2i2i−2i−2i2i-220000000000000000000000000000000000000000
χ724-4-44−4i4i4i−4i-2−4i4i4-422-2000000002i−2i−2i2i2i−2i-220000000000000000000000000000000000000000

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