Finite Group Databasebeta

← Group #70516

Character table — Group #70516

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222222222222444444444444666666666666666688888888888824242424
order1222444422344444444446661212121266121212121212121212128888888888888888888824242424242424248888
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
χ511111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ611111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ711111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ811111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−ii−ii−i
χ101111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−ii−ii
χ111111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111i−ii−iii−i−iii−i−i−ii−ii
χ121111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111−ii−ii−i−iii−i−iiii−ii−i
χ131111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiii−i−ii
χ141111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−iii−i
χ151111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1i−i−iiii−i−i−i−iii−iii−i
χ161111-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1−iii−i−i−iiiii−i−ii−i−ii
χ172222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ182222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ192222222222-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ202222222222-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ2122222222-2-2222-2-222-2-2-2-22222222-2-2-2-222-2-222-2-200000000000000000000000000000000
χ2222222222-2-22-2-222-2-222-2-22222222-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ2322222222-2-2-122-2-222-2-2-2-2-1-1-1-1-1-1-11111-1-111-1-11100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2422222222-2-2-122-2-222-2-2-2-2-1-1-1-1-1-1-11111-1-111-1-11100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2522222222-2-2-1-2-222-2-222-2-2-1-1-1-1-1-1-1111111-1-111-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ2622222222-2-2-1-2-222-2-222-2-2-1-1-1-1-1-1-1111111-1-111-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ272222-2-2-2-222222-2-2-2-222-2-2222-2-2-2-222-2-222-2-2-2-22200000000000000000000000000000000
χ282222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-222-2-2-2-22222-2-200000000000000000000000000000000
χ292222-2-2-2-222-122-2-2-2-222-2-2-1-1-11111-1-111-1-11111-1-1000000000000000000003−3−333−3−330000
χ302222-2-2-2-222-122-2-2-2-222-2-2-1-1-11111-1-111-1-11111-1-100000000000000000000−333−3−333−30000
χ312222-2-2-2-222-1-2-22222-2-2-2-2-1-1-11111-1-11111-1-1-1-111000000000000000000003−3−33−333−30000
χ322222-2-2-2-222-1-2-22222-2-2-2-2-1-1-11111-1-11111-1-1-1-11100000000000000000000−333−33−3−330000
χ332222-2-2-2-2-2-2-12222-2-2-2-222-1-1-1111111-1-1-1-1-1-1111100000000000000002i−2i2i−2i−i−iii−i−iii0000
χ342222-2-2-2-2-2-2-12222-2-2-2-222-1-1-1111111-1-1-1-1-1-111110000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ352222-2-2-2-2-2-2-1-2-2-2-2222222-1-1-1111111-1-11111-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ362222-2-2-2-2-2-2-1-2-2-2-2222222-1-1-1111111-1-11111-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ3722-2-222-2-22-22000000002-22-2-2-2-2222-22-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ3822-2-222-2-22-22000000002-22-2-2-2-2222-22-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ3922-2-222-2-2-22200000000-222-2-2-2-222-22-22000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ4022-2-222-2-2-22200000000-222-2-2-2-222-22-2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ4122-2-2-2-2222-2200000000-222-2-222-2-22-2-22000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ4222-2-2-2-2222-2200000000-222-2-222-2-22-2-2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ4322-2-2-2-222-222000000002-22-2-222-2-2-222-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ4422-2-2-2-222-222000000002-22-2-222-2-2-222-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ452-22-22i−2i2i−2i002002i−2i002-200-22-22i−2i2i−2i0000002i−2i002-22−22−2−i2i2−i2i2−i2i2−i2i22−22−20000000000000000
χ462-22-22i−2i2i−2i002002i−2i002-200-22-22i−2i2i−2i0000002i−2i002-2−22−22i2−i2i2−i2i2−i2i2−i2−22−220000000000000000
χ472-22-22i−2i2i−2i00200−2i2i00-2200-22-22i−2i2i−2i000000−2i2i00-222−22−2−i2i2−i2i2i2−i2i2−i2−22−220000000000000000
χ482-22-22i−2i2i−2i00200−2i2i00-2200-22-22i−2i2i−2i000000−2i2i00-22−22−22i2−i2i2−i2−i2i2−i2i22−22−20000000000000000
χ492-22-2−2i2i−2i2i002002i−2i00-2200-22-2−2i2i−2i2i0000002i−2i00-222−22−2i2−i2i2−i2−i2i2−i2i2−22−220000000000000000
χ502-22-2−2i2i−2i2i002002i−2i00-2200-22-2−2i2i−2i2i0000002i−2i00-22−22−22−i2i2−i2i2i2−i2i2−i22−22−20000000000000000
χ512-22-2−2i2i−2i2i00200−2i2i002-200-22-2−2i2i−2i2i000000−2i2i002-22−22−2i2−i2i2−i2i2−i2i2−i22−22−20000000000000000
χ522-22-2−2i2i−2i2i00200−2i2i002-200-22-2−2i2i−2i2i000000−2i2i002-2−22−22−i2i2−i2i2−i2i2−i2i2−22−220000000000000000
χ532-2-222i−2i−2i2i0022i−2i002-20000-2-22−2i2i2i−2i00002i−2i002-200−i2i2i2−i2−222−22−2−22i2−i2−i2i20000000000000000
χ542-2-222i−2i−2i2i0022i−2i002-20000-2-22−2i2i2i−2i00002i−2i002-200i2−i2−i2i22−2−22−222−2−i2i2i2−i20000000000000000
χ552-2-222i−2i−2i2i002−2i2i00-220000-2-22−2i2i2i−2i0000−2i2i00-2200−i2i2i2−i2−222−2−222−2−i2i2i2−i20000000000000000
χ562-2-222i−2i−2i2i002−2i2i00-220000-2-22−2i2i2i−2i0000−2i2i00-2200i2−i2−i2i22−2−222−2−22i2−i2−i2i20000000000000000
χ572-2-22−2i2i2i−2i0022i−2i00-220000-2-222i−2i−2i2i00002i−2i00-2200−i2i2i2−i22−2−222−2−22−i2i2i2−i20000000000000000
χ582-2-22−2i2i2i−2i0022i−2i00-220000-2-222i−2i−2i2i00002i−2i00-2200i2−i2−i2i2−222−2−222−2i2−i2−i2i20000000000000000
χ592-2-22−2i2i2i−2i002−2i2i002-20000-2-222i−2i−2i2i0000−2i2i002-200−i2i2i2−i22−2−22−222−2i2−i2−i2i20000000000000000
χ602-2-22−2i2i2i−2i002−2i2i002-20000-2-222i−2i−2i2i0000−2i2i002-200i2−i2−i2i2−222−22−2−22−i2i2i2−i20000000000000000
χ6144-4-444-4-44-4-2000000004-4-22222-2-2-22-220000000000000000000000000000000000000000
χ6244-4-444-4-4-44-200000000-44-22222-2-22-22-20000000000000000000000000000000000000000
χ6344-4-4-4-4444-4-200000000-44-222-2-222-222-20000000000000000000000000000000000000000
χ6444-4-4-4-444-44-2000000004-4-222-2-2222-2-220000000000000000000000000000000000000000
χ654-44-44i−4i4i−4i00-2004i−4i004-4002-22−2i2i−2i2i000000−2i2i00-2200000000000000000000000000000000
χ664-44-44i−4i4i−4i00-200−4i4i00-44002-22−2i2i−2i2i0000002i−2i002-200000000000000000000000000000000
χ674-44-4−4i4i−4i4i00-2004i−4i00-44002-222i−2i2i−2i000000−2i2i002-200000000000000000000000000000000
χ684-44-4−4i4i−4i4i00-200−4i4i004-4002-222i−2i2i−2i0000002i−2i00-2200000000000000000000000000000000
χ694-4-444i−4i−4i4i00-24i−4i004-4000022-22i−2i−2i2i0000−2i2i00-220000000000000000000000000000000000
χ704-4-444i−4i−4i4i00-2−4i4i00-44000022-22i−2i−2i2i00002i−2i002-20000000000000000000000000000000000
χ714-4-44−4i4i4i−4i00-24i−4i00-44000022-2−2i2i2i−2i0000−2i2i002-20000000000000000000000000000000000
χ724-4-44−4i4i4i−4i00-2−4i4i004-4000022-2−2i2i2i−2i00002i−2i00-220000000000000000000000000000000000

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