Finite Group Databasebeta

← Group #68939

Character table — Group #68939

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222222222222444444444444666666666666666688888888888824242424
order1222444422344666888888881212121266121224242424242424242222444488888888888824242424242424248888
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
χ91111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1i−ii−iii−i−iii−i−ii−ii−i
χ101111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−ii−ii
χ111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-11111i−ii−iii−i−iii−i−i−ii−ii
χ121111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-11111−ii−ii−i−iii−i−iiii−ii−i
χ131111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-11111i−i−iiii−i−i−i−iiii−i−ii
χ141111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−iii−i
χ151111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1111111-1-1-1-1i−i−iiii−i−i−i−iii−iii−i
χ161111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1111111-1-1-1-1−iii−i−i−iiiii−i−ii−i−ii
χ172222222222-122-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ182222222222-122-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ192222222222-122-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ202222222222-122-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ2122222222-2-22-2-2222000000002222-2-2-2-20000000022-2-2-2-222000000000000000000000000
χ2222222222-2-22-2-2222000000002222-2-2-2-200000000-2-22222-2-2000000000000000000000000
χ232222-2-2-2-2222-2-222200000000-2-2-2-222-2-2000000002222-2-2-2-2000000000000000000000000
χ242222-2-2-2-2222-2-222200000000-2-2-2-222-2-200000000-2-2-2-22222000000000000000000000000
χ252222-2-2-2-2-2-2-122-1-1-12222-2-2-2-2111111-1-1-1-1-1-1111100000000000000002i−2i2i−2i−i−iii−i−iii0000
χ262222-2-2-2-2-2-2-122-1-1-12222-2-2-2-2111111-1-1-1-1-1-111110000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ272222-2-2-2-2-2-2-122-1-1-1-2-2-2-22222111111-1-11111-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ282222-2-2-2-2-2-2-122-1-1-1-2-2-2-22222111111-1-11111-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ2922-2-22i2i−2i−2i002002-2-222−2−2−i2−i2i2i22i2i−2i−2i000022−2−2−i2−i2i2i2002-22i−2i00−i2−i2i2i222−2−20000000000000000
χ3022-2-22i2i−2i−2i002002-2-222−2−2−i2−i2i2i22i2i−2i−2i000022−2−2−i2−i2i2i200-22−2i2i00i2i2−i2−i2−2−2220000000000000000
χ3122-2-22i2i−2i−2i002002-2-2−2−222i2i2−i2−i22i2i−2i−2i0000−2−222i2i2−i2−i2002-22i−2i00i2i2−i2−i2−2−2220000000000000000
χ3222-2-22i2i−2i−2i002002-2-2−2−222i2i2−i2−i22i2i−2i−2i0000−2−222i2i2−i2−i200-22−2i2i00−i2−i2i2i222−2−20000000000000000
χ3322-2-2−2i−2i2i2i002002-2-222−2−2i2i2−i2−i2−2i−2i2i2i000022−2−2i2i2−i2−i2002-2−2i2i00i2i2−i2−i222−2−20000000000000000
χ3422-2-2−2i−2i2i2i002002-2-222−2−2i2i2−i2−i2−2i−2i2i2i000022−2−2i2i2−i2−i200-222i−2i00−i2−i2i2i2−2−2220000000000000000
χ3522-2-2−2i−2i2i2i002002-2-2−2−222−i2−i2i2i2−2i−2i2i2i0000−2−222−i2−i2i2i2002-2−2i2i00−i2−i2i2i2−2−2220000000000000000
χ3622-2-2−2i−2i2i2i002002-2-2−2−222−i2−i2i2i2−2i−2i2i2i0000−2−222−i2−i2i2i200-222i−2i00i2i2−i2−i222−2−20000000000000000
χ372-22-22i−2i2i−2i00200-22-2−i2i2−i2i22−22−22i−2i2i−2i0000−i2i2−i2i22−22−22-200002i−2i−i2i2−i2i22−22−20000000000000000
χ382-22-22i−2i2i−2i00200-22-2−i2i2−i2i22−22−22i−2i2i−2i0000−i2i2−i2i22−22−2-220000−2i2ii2−i2i2−i2−22−220000000000000000
χ392-22-22i−2i2i−2i00200-22-2i2−i2i2−i2−22−222i−2i2i−2i0000i2−i2i2−i2−22−222-200002i−2ii2−i2i2−i2−22−220000000000000000
χ402-22-22i−2i2i−2i00200-22-2i2−i2i2−i2−22−222i−2i2i−2i0000i2−i2i2−i2−22−22-220000−2i2i−i2i2−i2i22−22−20000000000000000
χ412-22-2−2i2i−2i2i00200-22-2−i2i2−i2i2−22−22−2i2i−2i2i0000−i2i2−i2i2−22−222-20000−2i2i−i2i2−i2i2−22−220000000000000000
χ422-22-2−2i2i−2i2i00200-22-2−i2i2−i2i2−22−22−2i2i−2i2i0000−i2i2−i2i2−22−22-2200002i−2ii2−i2i2−i22−22−20000000000000000
χ432-22-2−2i2i−2i2i00200-22-2i2−i2i2−i22−22−2−2i2i−2i2i0000i2−i2i2−i22−22−22-20000−2i2ii2−i2i2−i22−22−20000000000000000
χ442-22-2−2i2i−2i2i00200-22-2i2−i2i2−i22−22−2−2i2i−2i2i0000i2−i2i2−i22−22−2-2200002i−2i−i2i2−i2i2−22−220000000000000000
χ452-2-222-2-222-222-2-2-222i−2i−2i2i−2i2i2i−2i2-2-222-22-22i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ462-2-222-2-222-222-2-2-22−2i2i2i−2i2i−2i−2i2i2-2-222-22-2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ472-2-222-2-222-2-12-211-12i−2i−2i2i−2i2i2i−2i-111-1-11-11−iii−ii−i−ii00000000000000000000−i3i3−i3i33−33−30000
χ482-2-222-2-222-2-12-211-12i−2i−2i2i−2i2i2i−2i-111-1-11-11−iii−ii−i−ii00000000000000000000i3−i3i3−i3−33−330000
χ492-2-222-2-222-2-12-211-1−2i2i2i−2i2i−2i−2i2i-111-1-11-11i−i−ii−iii−i00000000000000000000−i3i3−i3i3−33−330000
χ502-2-222-2-222-2-12-211-1−2i2i2i−2i2i−2i−2i2i-111-1-11-11i−i−ii−iii−i00000000000000000000i3−i3i3−i33−33−30000
χ512-2-222-2-22-222-22-2-22000000002-2-22-22-2200000000000000002-2-222-2-220000000000000000
χ522-2-222-2-22-222-22-2-22000000002-2-22-22-220000000000000000-222-2-222-20000000000000000
χ532-2-22-222-22-22-22-2-2200000000-222-22-2-2200000000000000002-2-22-222-20000000000000000
χ542-2-22-222-22-22-22-2-2200000000-222-22-2-220000000000000000-222-22-2-220000000000000000
χ552-2-22-222-2-2222-2-2-222i−2i−2i2i2i−2i−2i2i-222-2-222-22i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ562-2-22-222-2-2222-2-2-22−2i2i2i−2i−2i2i2i−2i-222-2-222-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ572-2-22-222-2-22-12-211-12i−2i−2i2i2i−2i−2i2i1-1-111-1-11−iii−i−iii−i000000000000000000003−3−33i3−i3−i3i30000
χ582-2-22-222-2-22-12-211-12i−2i−2i2i2i−2i−2i2i1-1-111-1-11−iii−i−iii−i00000000000000000000−333−3−i3i3i3−i30000
χ592-2-22-222-2-22-12-211-1−2i2i2i−2i−2i2i2i−2i1-1-111-1-11i−i−iii−i−ii000000000000000000003−3−33−i3i3i3−i30000
χ602-2-22-222-2-22-12-211-1−2i2i2i−2i−2i2i2i−2i1-1-111-1-11i−i−iii−i−ii00000000000000000000−333−3i3−i3−i3i30000
χ6144444444-4-4-2-4-4-2-2-200000000-2-2-2-222220000000000000000000000000000000000000000
χ624444-4-4-4-444-2-4-4-2-2-2000000002222-2-2220000000000000000000000000000000000000000
χ6344-4-44i4i−4i−4i00-200-2222222−22−22−2i2−2i22i22i2−2i−2i2i2i0000−2−222i2i2−i2−i200000000000000000000000000000000
χ6444-4-44i4i−4i−4i00-200-222−22−2222222i22i2−2i2−2i2−2i−2i2i2i000022−2−2−i2−i2i2i200000000000000000000000000000000
χ6544-4-4−4i−4i4i4i00-200-2222222−22−222i22i2−2i2−2i22i2i−2i−2i0000−2−222−i2−i2i2i200000000000000000000000000000000
χ6644-4-4−4i−4i4i4i00-200-222−22−222222−2i2−2i22i22i22i2i−2i−2i000022−2−2i2i2−i2−i200000000000000000000000000000000
χ674-44-44i−4i4i−4i00-2002-22−2i22i2−2i22i222−2222−22−2i2i−2i2i0000i2−i2i2−i2−22−2200000000000000000000000000000000
χ684-44-44i−4i4i−4i00-2002-222i2−2i22i2−2i2−2222−2222−2i2i−2i2i0000−i2i2−i2i22−22−200000000000000000000000000000000
χ694-44-4−4i4i−4i4i00-2002-22−2i22i2−2i22i2−2222−22222i−2i2i−2i0000i2−i2i2−i22−22−200000000000000000000000000000000
χ704-44-4−4i4i−4i4i00-2002-222i2−2i22i2−2i222−2222−222i−2i2i−2i0000−i2i2−i2i2−22−2200000000000000000000000000000000
χ714-4-444-4-44-44-2-4422-200000000-222-22-22-20000000000000000000000000000000000000000
χ724-4-44-444-44-4-2-4422-2000000002-2-22-222-20000000000000000000000000000000000000000

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