Finite Group Databasebeta

← Group #69615

Character table — Group #69615

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222222222222444444444444666666666666666688888888888824242424
order12222222344444444444466666661212121212121212121212128888888888888888444412121212121212122244
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
χ911-11-11-1-111-1ii−i−iii−i−i1-11-1-11-11-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i1-1i−i
χ1011-11-11-1-111-1ii−i−iii−i−i1-11-1-11-11-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-11−ii
χ1111-11-11-1-111-1ii−i−iii−i−i1-11-1-11-11-111-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii1-1i−i11-1-1ii−i−i-11−ii
χ1211-11-11-1-111-1ii−i−iii−i−i1-11-1-11-11-111-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii-11−ii-1-111−i−iii1-1i−i
χ1311-11-11-1-111-1−i−iii−i−iii1-11-1-11-11-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii1-1−ii
χ1411-11-11-1-111-1−i−iii−i−iii1-11-1-11-11-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-11i−i
χ1511-11-11-1-111-1−i−iii−i−iii1-11-1-11-11-111-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i1-1−ii11-1-1−i−iii-11i−i
χ1611-11-11-1-111-1−i−iii−i−iii1-11-1-11-11-111-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i-11i−i-1-111ii−i−i1-1−ii
χ17222222222-2-22222-2-2-2-2-2-22222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ18222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ1922222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ2022222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ2122222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ2222222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ2322222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2422222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2522222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ2622222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ27222-2-2-22-22002i−2i2i−2i00000022-2-2-2-2200002i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000
χ28222-2-2-22-22002i−2i2i−2i00000022-2-2-2-2200002i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000
χ29222-2-2-22-2200−2i2i−2i2i00000022-2-2-2-220000−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000000000000000
χ30222-2-2-22-2200−2i2i−2i2i00000022-2-2-2-220000−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000
χ3122-22-22-2-22-222i2i−2i−2i−2i−2i2i2i-222-2-22-22-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ3222-22-22-2-22-22−2i−2i2i2i2i2i−2i−2i-222-2-22-22-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ3322-22-22-2-2-12-22i2i−2i−2i2i2i−2i−2i2-2-111-11-11-1-111−i−iii−i−iii00000000000000002-22i−2i-1-111−i−iii0000
χ3422-22-22-2-2-12-22i2i−2i−2i2i2i−2i−2i2-2-111-11-11-1-111−i−iii−i−iii0000000000000000-22−2i2i11-1-1ii−i−i0000
χ3522-22-22-2-2-12-2−2i−2i2i2i−2i−2i2i2i2-2-111-11-11-1-111ii−i−iii−i−i00000000000000002-2−2i2i-1-111ii−i−i0000
χ3622-22-22-2-2-12-2−2i−2i2i2i−2i−2i2i2i2-2-111-11-11-1-111ii−i−iii−i−i0000000000000000-222i−2i11-1-1−i−iii0000
χ3722-22-22-2-2-1-222i2i−2i−2i−2i−2i2i2i-22-111-11-1111-1-1−i−iiiii−i−i00000000000000000000−i3i3i3−i33−3−330000
χ3822-22-22-2-2-1-222i2i−2i−2i−2i−2i2i2i-22-111-11-1111-1-1−i−iiiii−i−i00000000000000000000i3−i3−i3i3−333−30000
χ3922-22-22-2-2-1-22−2i−2i2i2i2i2i−2i−2i-22-111-11-1111-1-1ii−i−i−i−iii00000000000000000000−i3i3i3−i3−333−30000
χ4022-22-22-2-2-1-22−2i−2i2i2i2i2i−2i−2i-22-111-11-1111-1-1ii−i−i−i−iii00000000000000000000i3−i3−i3i33−3−330000
χ4122-2-22-2-222002-2-220000002-22-22-2-200002-2-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ4222-2-22-2-222002-2-220000002-22-22-2-200002-2-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ4322-2-22-2-22200-222-20000002-22-22-2-20000-222-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ4422-2-22-2-22200-222-20000002-22-22-2-20000-222-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ452-222-2-2-2222-200000000-22-2222-2-2-22-22-2000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ462-222-2-2-2222-200000000-22-2222-2-2-22-22-200000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ472-222-2-2-222-22000000002-2-2222-2-2-2-22-2200000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ482-222-2-2-222-22000000002-2-2222-2-2-2-22-220000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ492-22-222-2-220000002i−2i2i−2i00-22-2-222-2000000002i−2i2i−2i2−2−222−2−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ502-22-222-2-220000002i−2i2i−2i00-22-2-222-2000000002i−2i2i−2i−222−2−222−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ512-22-222-2-22000000−2i2i−2i2i00-22-2-222-200000000−2i2i−2i2i2−2−222−2−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ522-22-222-2-22000000−2i2i−2i2i00-22-2-222-200000000−2i2i−2i2i−222−2−222−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ532-2-222-22-222200000000-2-2-2-2-222-222-2-22000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ542-2-222-22-222200000000-2-2-2-2-222-222-2-2200000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ552-2-222-22-22-2-20000000022-2-2-222-22-222-200000000000000002-22-2-22-220000000000000000
χ562-2-222-22-22-2-20000000022-2-2-222-22-222-20000000000000000-22-222-22-20000000000000000
χ572-2-2-2-222220000002-2-2200-2-22-2-222000000002-2-222−2−22−222−2−222−22−2−220000000000000000
χ582-2-2-2-222220000002-2-2200-2-22-2-222000000002-2-22−222−22−2−222−2−22−222−20000000000000000
χ592-2-2-2-22222000000-222-200-2-22-2-22200000000-222-22−2−22−222−22−2−22−222−20000000000000000
χ602-2-2-2-22222000000-222-200-2-22-2-22200000000-222-2−222−22−2−22−222−22−2−220000000000000000
χ61444-4-4-44-4-2004i−4i4i−4i000000-2-22222-20000−2i2i−2i2i000000000000000000000000000000000000
χ62444-4-4-44-4-200−4i4i−4i4i000000-2-22222-200002i−2i2i−2i000000000000000000000000000000000000
χ6344-4-44-4-44-2004-4-44000000-22-22-2220000-222-2000000000000000000000000000000000000
χ6444-4-44-4-44-200-444-4000000-22-22-22200002-2-22000000000000000000000000000000000000
χ654-444-4-4-44-24-400000000-442-2-2-2222-22-220000000000000000000000000000000000000000
χ664-444-4-4-44-2-44000000004-42-2-2-22222-22-20000000000000000000000000000000000000000
χ674-44-444-4-4-20000004i−4i4i−4i002-222-2-2200000000−2i2i−2i2i00000000000000000000000000000000
χ684-44-444-4-4-2000000−4i4i−4i4i002-222-2-22000000002i−2i2i−2i00000000000000000000000000000000
χ694-4-444-44-4-24400000000-4-4222-2-22-2-222-20000000000000000000000000000000000000000
χ704-4-444-44-4-2-4-40000000044222-2-22-22-2-220000000000000000000000000000000000000000
χ714-4-4-4-4444-20000004-4-440022-222-2-200000000-222-200000000000000000000000000000000
χ724-4-4-4-4444-2000000-444-40022-222-2-2000000002-2-2200000000000000000000000000000000

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