Finite Group Databasebeta

← Group #76288

Character table — Group #76288

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222222222222444444444444666666666666666688888888888824242424
order12222222344444444444466666661212121212121212121212122222444444444444444412121212121212124444
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
χ51111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111
χ61111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1
χ71111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-1
χ81111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-111
χ9111111111-1-1-1-11111-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-11-11-1
χ10111111111-1-1-1-11111-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-11-11
χ11111111111-1-1-1-11111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-111-1-1-11-11
χ12111111111-1-1-1-11111-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-111-1-1111-11-1
χ13111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111-111-1
χ14111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-11-1-11
χ15111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-1111-1-11
χ16111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-1-111-1
χ1722222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ1822222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ1922222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ2022222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ2122222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-1111100000000000000002-22-2-1-111-1-1110000
χ2222222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-111110000000000000000-22-2211-1-111-1-10000
χ2322222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-100000000000000002-2-22-1-11111-1-10000
χ2422222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-10000000000000000-222-211-1-1-1-1110000
χ25222-22-2-2-22000022-2-2000022-22-2-2-2000022-2-2000022-2-2000022-2-200000000000000000000
χ26222-22-2-2-22000022-2-2000022-22-2-2-2000022-2-20000-2-2220000-2-22200000000000000000000
χ27222-22-2-2-220000-2-222000022-22-2-2-20000-2-222000022-2-20000-2-22200000000000000000000
χ28222-22-2-2-220000-2-222000022-22-2-2-20000-2-2220000-2-222000022-2-200000000000000000000
χ2922-22-22-2-2222-2-2000000002-22-22-2-222-2-2000000002-22-222-2-2000000000000000000000000
χ3022-22-22-2-2222-2-2000000002-22-22-2-222-2-200000000-22-22-2-222000000000000000000000000
χ3122-22-22-2-22-2-222000000002-22-22-2-2-2-222000000002-22-2-2-222000000000000000000000000
χ3222-22-22-2-22-2-222000000002-22-22-2-2-2-22200000000-22-2222-2-2000000000000000000000000
χ3322-2-2-2-22220000000022-2-22-2-2-2-2220000000022-2-22-2-220000000022-2-20000000000000000
χ3422-2-2-2-22220000000022-2-22-2-2-2-2220000000022-2-2-222-200000000-2-2220000000000000000
χ3522-2-2-2-222200000000-2-2222-2-2-2-22200000000-2-2222-2-2200000000-2-2220000000000000000
χ3622-2-2-2-222200000000-2-2222-2-2-2-22200000000-2-222-222-20000000022-2-20000000000000000
χ372-222-2-2-22200002i−2i2i−2i0000-222-2-2-2200002i−2i2i−2i000000002i−2i2i−2i00002-22-20000000000000000
χ382-222-2-2-22200002i−2i2i−2i0000-222-2-2-2200002i−2i2i−2i00000000−2i2i−2i2i0000-22-220000000000000000
χ392-222-2-2-2220000−2i2i−2i2i0000-222-2-2-220000−2i2i−2i2i000000002i−2i2i−2i0000-22-220000000000000000
χ402-222-2-2-2220000−2i2i−2i2i0000-222-2-2-220000−2i2i−2i2i00000000−2i2i−2i2i00002-22-20000000000000000
χ412-22-2-222-222-22-22i−2i−2i2i2i−2i2i−2i-22-2-222-22-22-22i−2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ422-22-2-222-222-22-2−2i2i2i−2i−2i2i−2i2i-22-2-222-22-22-2−2i2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ432-22-2-222-22-22-222i−2i−2i2i−2i2i−2i2i-22-2-222-2-22-222i−2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ442-22-2-222-22-22-22−2i2i2i−2i2i−2i2i−2i-22-2-222-2-22-22−2i2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ452-22-2-222-2-12-22-22i−2i−2i2i2i−2i2i−2i1-111-1-11-11-11−iii−i−ii−ii00000000000000000000−i3i3−i3i33−33−30000
χ462-22-2-222-2-12-22-22i−2i−2i2i2i−2i2i−2i1-111-1-11-11-11−iii−i−ii−ii00000000000000000000i3−i3i3−i3−33−330000
χ472-22-2-222-2-12-22-2−2i2i2i−2i−2i2i−2i2i1-111-1-11-11-11i−i−iii−ii−i00000000000000000000−i3i3−i3i3−33−330000
χ482-22-2-222-2-12-22-2−2i2i2i−2i−2i2i−2i2i1-111-1-11-11-11i−i−iii−ii−i00000000000000000000i3−i3i3−i33−33−30000
χ492-22-2-222-2-1-22-222i−2i−2i2i−2i2i−2i2i1-111-1-111-11-1−iii−ii−ii−i00000000000000000000−i3i3i3−i33−3−330000
χ502-22-2-222-2-1-22-222i−2i−2i2i−2i2i−2i2i1-111-1-111-11-1−iii−ii−ii−i00000000000000000000i3−i3−i3i3−333−30000
χ512-22-2-222-2-1-22-22−2i2i2i−2i2i−2i2i−2i1-111-1-111-11-1i−i−ii−ii−ii00000000000000000000−i3i3i3−i3−333−30000
χ522-22-2-222-2-1-22-22−2i2i2i−2i2i−2i2i−2i1-111-1-111-11-1i−i−ii−ii−ii00000000000000000000i3−i3−i3i33−3−330000
χ532-2-222-22-22000000002i−2i−2i2i-2-222-22-2000000002i−2i−2i2i00002i−2i−2i2i2-22-200000000000000000000
χ542-2-222-22-22000000002i−2i−2i2i-2-222-22-2000000002i−2i−2i2i0000−2i2i2i−2i-22-2200000000000000000000
χ552-2-222-22-2200000000−2i2i2i−2i-2-222-22-200000000−2i2i2i−2i00002i−2i−2i2i-22-2200000000000000000000
χ562-2-222-22-2200000000−2i2i2i−2i-2-222-22-200000000−2i2i2i−2i0000−2i2i2i−2i2-22-200000000000000000000
χ572-2-2-222-2222-2-2200000000-2-2-222-222-2-2200000000000000002-2-22-222-20000000000000000
χ582-2-2-222-2222-2-2200000000-2-2-222-222-2-220000000000000000-222-22-2-220000000000000000
χ592-2-2-222-222-222-200000000-2-2-222-22-222-200000000000000002-2-222-2-220000000000000000
χ602-2-2-222-222-222-200000000-2-2-222-22-222-20000000000000000-222-2-222-20000000000000000
χ61444-44-4-4-4-2000044-4-40000-2-22-22220000-2-222000000000000000000000000000000000000
χ62444-44-4-4-4-20000-4-4440000-2-22-2222000022-2-2000000000000000000000000000000000000
χ6344-44-44-4-4-244-4-400000000-22-22-222-2-2220000000000000000000000000000000000000000
χ6444-44-44-4-4-2-4-44400000000-22-22-22222-2-20000000000000000000000000000000000000000
χ6544-4-4-4-444-20000000044-4-4-22222-2-200000000-2-22200000000000000000000000000000000
χ6644-4-4-4-444-200000000-4-444-22222-2-20000000022-2-200000000000000000000000000000000
χ674-444-4-4-44-200004i−4i4i−4i00002-2-2222-20000−2i2i−2i2i000000000000000000000000000000000000
χ684-444-4-4-44-20000−4i4i−4i4i00002-2-2222-200002i−2i2i−2i000000000000000000000000000000000000
χ694-4-444-44-4-2000000004i−4i−4i4i22-2-22-2200000000−2i2i2i−2i00000000000000000000000000000000
χ704-4-444-44-4-200000000−4i4i4i−4i22-2-22-22000000002i−2i−2i2i00000000000000000000000000000000
χ714-4-4-444-44-24-4-4400000000222-2-22-2-222-20000000000000000000000000000000000000000
χ724-4-4-444-44-2-444-400000000222-2-22-22-2-220000000000000000000000000000000000000000

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