Finite Group Databasebeta

← Group #68848

Character table — Group #68848

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222222222222444444444444666666666666666688888888888824242424
order12222222344446666666888888881212121224242424242424244444444488888888444412121212121212124444
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
χ511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ911-1-111-1-11-1-11111-1-11-1-11111-1-1-1-11-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−ii−ii−i
χ1011-1-111-1-11-1-11111-1-11-1-11111-1-1-1-11-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−ii−ii
χ1111-1-111-1-11-1-11111-1-11-1-11111-1-1-1-11-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111i−ii−iii−i−iii−i−i−ii−ii
χ1211-1-111-1-11-1-11111-1-11-1-11111-1-1-1-11-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111−ii−ii−i−iii−i−iiii−ii−i
χ1311-1-111-1-11-1-11111-1-11-1-1-1-1-1-111111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiii−i−ii
χ1411-1-111-1-11-1-11111-1-11-1-1-1-1-1-111111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−iii−i
χ1511-1-111-1-11-1-11111-1-11-1-1-1-1-1-111111-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1i−i−iiii−i−i−i−iii−iii−i
χ1611-1-111-1-11-1-11111-1-11-1-1-1-1-1-111111-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1−iii−i−i−iiiii−i−ii−i−ii
χ17222222222-2-2-2-2222222200000000-2-2-2-20000000022-2-222-2-2000000000000000000000000
χ18222222222-2-2-2-2222222200000000-2-2-2-200000000-2-222-2-222000000000000000000000000
χ1922222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ2022222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ2122222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ2222222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ23222-2-2-22-222-22-2-2-22-222-200000000-22-2200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ24222-2-2-22-222-22-2-2-22-222-200000000-22-220000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ25222-2-2-22-22-22-22-2-22-222-22i2i−2i−2i2i2i−2i−2i2-22-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ26222-2-2-22-22-22-22-2-22-222-2−2i−2i2i2i−2i−2i2i2i2-22-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ27222-2-2-22-2-1-22-2211-11-1-112i2i−2i−2i2i2i−2i−2i-11-11−i−iii−i−iii00000000000000000000−i3i3−i3i33−33−30000
χ28222-2-2-22-2-1-22-2211-11-1-112i2i−2i−2i2i2i−2i−2i-11-11−i−iii−i−iii00000000000000000000i3−i3i3−i3−33−330000
χ29222-2-2-22-2-1-22-2211-11-1-11−2i−2i2i2i−2i−2i2i2i-11-11ii−i−iii−i−i00000000000000000000−i3i3−i3i3−33−330000
χ30222-2-2-22-2-1-22-2211-11-1-11−2i−2i2i2i−2i−2i2i2i-11-11ii−i−iii−i−i00000000000000000000i3−i3i3−i33−33−30000
χ3122-22-2-2-2222-2-22-2-2-222-222i2i−2i−2i−2i−2i2i2i22-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ3222-22-2-2-2222-2-22-2-2-222-22−2i−2i2i2i2i2i−2i−2i22-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ3322-22-2-2-222-222-2-2-2-222-2200000000-2-22200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ3422-22-2-2-222-222-2-2-2-222-2200000000-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ3522-22-2-2-22-12-2-22111-1-11-12i2i−2i−2i−2i−2i2i2i-1-111−i−iiiii−i−i000000000000000000003−3−33i3−i3−i3i30000
χ3622-22-2-2-22-12-2-22111-1-11-12i2i−2i−2i−2i−2i2i2i-1-111−i−iiiii−i−i00000000000000000000−333−3−i3i3i3−i30000
χ3722-22-2-2-22-12-2-22111-1-11-1−2i−2i2i2i2i2i−2i−2i-1-111ii−i−i−i−iii000000000000000000003−3−33−i3i3i3−i30000
χ3822-22-2-2-22-12-2-22111-1-11-1−2i−2i2i2i2i2i−2i−2i-1-111ii−i−i−i−iii00000000000000000000−333−3i3−i3−i3i30000
χ3922-2-222-2-2222-2-222-2-22-2-200000000-222-20000000022-2-2-2-222000000000000000000000000
χ4022-2-222-2-2222-2-222-2-22-2-200000000-222-200000000-2-22222-2-2000000000000000000000000
χ4122-2-222-2-2-1-2-222-1-111-1112222-2-2-2-2-111-1-1-1-1-1111100000000000000002i−2i2i−2i−i−iii−i−iii0000
χ4222-2-222-2-2-1-2-222-1-111-1112222-2-2-2-2-111-1-1-1-1-111110000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ4322-2-222-2-2-1-2-222-1-111-111-2-2-2-22222-111-11111-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ4422-2-222-2-2-1-2-222-1-111-111-2-2-2-22222-111-11111-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ452-2222-2-2-2200002-2-2-2-2222−22−22−22−200002−22−22−22−2002i−2i002i−2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ462-2222-2-2-2200002-2-2-2-2222−22−22−22−200002−22−22−22−200−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ472-2222-2-2-2200002-2-2-2-222−22−22−22−220000−22−22−22−22002i−2i002i−2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ482-2222-2-2-2200002-2-2-2-222−22−22−22−220000−22−22−22−2200−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ492-22-2-22-2220000-22-22-22-2−i2i2i2−i2−i2i2i2−i20000−i2i2i2−i2−i2i2i2−i22i−2i002i−2i002−2−222−2−220000000000000000
χ502-22-2-22-2220000-22-22-22-2−i2i2i2−i2−i2i2i2−i20000−i2i2i2−i2−i2i2i2−i2−2i2i00−2i2i00−222−2−222−20000000000000000
χ512-22-2-22-2220000-22-22-22-2i2−i2−i2i2i2−i2−i2i20000i2−i2−i2i2i2−i2−i2i22i−2i002i−2i00−222−2−222−20000000000000000
χ522-22-2-22-2220000-22-22-22-2i2−i2−i2i2i2−i2−i2i20000i2−i2−i2i2i2−i2−i2i2−2i2i00−2i2i002−2−222−2−220000000000000000
χ532-2-22-222-220000-222-2-2-22−i2i2i2−i2i2−i2−i2i20000−i2i2i2−i2i2−i2−i2i22i−2i00−2i2i002−2−22−222−20000000000000000
χ542-2-22-222-220000-222-2-2-22−i2i2i2−i2i2−i2−i2i20000−i2i2i2−i2i2−i2−i2i2−2i2i002i−2i00−222−22−2−220000000000000000
χ552-2-22-222-220000-222-2-2-22i2−i2−i2i2−i2i2i2−i20000i2−i2−i2i2−i2i2i2−i22i−2i00−2i2i00−222−22−2−220000000000000000
χ562-2-22-222-220000-222-2-2-22i2−i2−i2i2−i2i2i2−i20000i2−i2−i2i2−i2i2i2−i2−2i2i002i−2i002−2−22−222−20000000000000000
χ572-2-2-22-222200002-222-2-2-22−22−2−22−2200002−22−2−22−22002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ582-2-2-22-222200002-222-2-2-22−22−2−22−2200002−22−2−22−2200−2i2i002i−2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ592-2-2-22-222200002-222-2-2-2−22−222−22−20000−22−222−22−2002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ602-2-2-22-222200002-222-2-2-2−22−222−22−20000−22−222−22−200−2i2i002i−2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-20000000022220000000000000000000000000000000000000000
χ62444-4-4-44-4-24-44-422-22-2-22000000002-22-20000000000000000000000000000000000000000
χ6344-44-4-4-44-2-444-4222-2-22-20000000022-2-20000000000000000000000000000000000000000
χ6444-4-444-4-4-244-4-4-2-222-222000000002-2-220000000000000000000000000000000000000000
χ654-4444-4-4-4-20000-22222-2-222−2222−2222−2222−220000−22−22−22−2200000000000000000000000000000000
χ664-4444-4-4-4-20000-22222-2-2−2222−2222−2222−222200002−22−22−22−200000000000000000000000000000000
χ674-44-4-44-44-200002-22-22-22−2i22i22i2−2i2−2i22i22i2−2i20000i2−i2−i2i2i2−i2−i2i200000000000000000000000000000000
χ684-44-4-44-44-200002-22-22-222i2−2i2−2i22i22i2−2i2−2i22i20000−i2i2i2−i2−i2i2i2−i200000000000000000000000000000000
χ694-4-44-444-4-200002-2-2222-2−2i22i22i2−2i22i2−2i2−2i22i20000i2−i2−i2i2−i2i2i2−i200000000000000000000000000000000
χ704-4-44-444-4-200002-2-2222-22i2−2i2−2i22i2−2i22i22i2−2i20000−i2i2i2−i2i2−i2−i2i200000000000000000000000000000000
χ714-4-4-44-444-20000-22-2-222222−2222−22−2222−22220000−22−222−22−200000000000000000000000000000000
χ724-4-4-44-444-20000-22-2-2222−2222−222222−2222−2200002−22−2−22−2200000000000000000000000000000000

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