Finite Group Databasebeta

← Group #70607

Character table — Group #70607

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
χ91-1-1111-1-11-1-11111-1-1-11-11111-1-1-1-11-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−ii−ii−i
χ101-1-1111-1-11-1-11111-1-1-11-11111-1-1-1-11-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−ii−ii
χ111-1-1111-1-11-1-11111-1-1-11-11111-1-1-1-11-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111i−ii−iii−i−iii−i−i−ii−ii
χ121-1-1111-1-11-1-11111-1-1-11-11111-1-1-1-11-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111−ii−ii−i−iii−i−iiii−ii−i
χ131-1-1111-1-11-1-11111-1-1-11-1-1-1-1-111111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiii−i−ii
χ141-1-1111-1-11-1-11111-1-1-11-1-1-1-1-111111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−iii−i
χ151-1-1111-1-11-1-11111-1-1-11-1-1-1-1-111111-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1i−i−iiii−i−i−i−iii−iii−i
χ161-1-1111-1-11-1-11111-1-1-11-1-1-1-1-111111-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1−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
χ232222-2-2-2-222-22-2-2-222-22-222-2-222-2-2-22-2222-2-222-2-200000000000000000000000000000000
χ242222-2-2-2-222-22-2-2-222-22-2-2-222-2-222-22-22-2-222-2-22200000000000000000000000000000000
χ252222-2-2-2-22-22-22-2-222-22-2000000002-22-2000000000000000022-2-222-2-20000000000000000
χ262222-2-2-2-22-22-22-2-222-22-2000000002-22-20000000000000000-2-222-2-2220000000000000000
χ272222-2-2-2-2-12-22-211-1-11-1122-2-222-2-21-11-1-1-111-1-111000000000000000000003−33−33−33−30000
χ282222-2-2-2-2-12-22-211-1-11-1122-2-222-2-21-11-1-1-111-1-11100000000000000000000−33−33−33−330000
χ292222-2-2-2-2-12-22-211-1-11-11-2-222-2-2221-11-111-1-111-1-1000000000000000000003−33−3−33−330000
χ302222-2-2-2-2-12-22-211-1-11-11-2-222-2-2221-11-111-1-111-1-100000000000000000000−33−333−33−30000
χ3122-2-22-22-2200002-22-2-2-222−22−22−22−200002−22−22−22−2002i−2i002i−2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ3222-2-22-22-2200002-22-2-2-222−22−22−22−200002−22−22−22−200−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ3322-2-22-22-2200002-22-2-2-22−22−22−22−220000−22−22−22−22002i−2i002i−2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ3422-2-22-22-2200002-22-2-2-22−22−22−22−220000−22−22−22−2200−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ3522-2-2-22-2220000-222-22-2-22−2−222−2−2200002−2−222−2−222i−2i002i−2i00−i2i2i2−i2−i2i2i2−i20000000000000000
χ3622-2-2-22-2220000-222-22-2-22−2−222−2−2200002−2−222−2−22−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i20000000000000000
χ3722-2-2-22-2220000-222-22-2-2−222−2−222−20000−222−2−222−22i−2i002i−2i00i2−i2−i2i2i2−i2−i2i20000000000000000
χ3822-2-2-22-2220000-222-22-2-2−222−2−222−20000−222−2−222−2−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i20000000000000000
χ392-22-22-2-22200002-2-222-2-22−22−2−22−2200002−22−2−22−22002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ402-22-22-2-22200002-2-222-2-22−22−2−22−2200002−22−2−22−2200−2i2i002i−2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ412-22-22-2-22200002-2-222-2-2−22−222−22−20000−22−222−22−2002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ422-22-22-2-22200002-2-222-2-2−22−222−22−20000−22−222−22−200−2i2i002i−2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ432-22-2-222-220000-22-22-2-222−2−22−222−200002−2−22−222−22i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ442-22-2-222-220000-22-22-2-222−2−22−222−200002−2−22−222−2−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ452-22-2-222-220000-22-22-2-22−222−22−2−220000−222−22−2−222i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ462-22-2-222-220000-22-22-2-22−222−22−2−220000−222−22−2−22−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ472-2-2222-2-2222-2-222-2-2-22-200000000-222-20000000022-2-2-2-222000000000000000000000000
χ482-2-2222-2-2222-2-222-2-2-22-200000000-222-200000000-2-22222-2-2000000000000000000000000
χ492-2-2222-2-2-1-2-222-1-1111-112222-2-2-2-2-111-1-1-1-1-1111100000000000000002i−2i2i−2i−i−iii−i−iii0000
χ502-2-2222-2-2-1-2-222-1-1111-112222-2-2-2-2-111-1-1-1-1-111110000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ512-2-2222-2-2-1-2-222-1-1111-11-2-2-2-22222-111-11111-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ522-2-2222-2-2-1-2-222-1-1111-11-2-2-2-22222-111-11111-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ532-2-22-2-22222-2-22-2-2-2-22220000000022-2-2000000000000000022-2-2-2-2220000000000000000
χ542-2-22-2-22222-2-22-2-2-2-22220000000022-2-20000000000000000-2-22222-2-20000000000000000
χ552-2-22-2-2222-222-2-2-2-2-222222-2-2-2-222-2-22222-2-2-2-22200000000000000000000000000000000
χ562-2-22-2-2222-222-2-2-2-2-2222-2-22222-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ572-2-22-2-222-1-222-21111-1-1-122-2-2-2-22211-1-1-1-11111-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ582-2-22-2-222-1-222-21111-1-1-122-2-2-2-22211-1-1-1-11111-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ592-2-22-2-222-1-222-21111-1-1-1-2-22222-2-211-1-111-1-1-1-11100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ602-2-22-2-222-1-222-21111-1-1-1-2-22222-2-211-1-111-1-1-1-11100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-20000000022220000000000000000000000000000000000000000
χ624444-4-4-4-4-2-44-4422-2-22-2200000000-22-220000000000000000000000000000000000000000
χ6344-4-44-44-4-20000-22-2222-222−2222−2222−2222−220000−22−22−22−2200000000000000000000000000000000
χ6444-4-44-44-4-20000-22-2222-2−2222−2222−2222−222200002−22−22−22−200000000000000000000000000000000
χ6544-4-4-44-44-200002-2-22-22222−22−222222−22−22220000−222−2−222−200000000000000000000000000000000
χ6644-4-4-44-44-200002-2-22-222−222222−22−222222−2200002−2−222−2−2200000000000000000000000000000000
χ674-44-44-4-44-20000-222-2-22222−2222−22−2222−22220000−22−222−22−200000000000000000000000000000000
χ684-44-44-4-44-20000-222-2-222−2222−222222−2222−2200002−22−2−22−2200000000000000000000000000000000
χ694-44-4-444-4-200002-22-222-222−22−2222−222222−220000−222−22−2−2200000000000000000000000000000000
χ704-44-4-444-4-200002-22-222-2−222222−2222−22−222200002−2−22−222−200000000000000000000000000000000
χ714-4-4444-4-4-244-4-4-2-2222-22000000002-2-220000000000000000000000000000000000000000
χ724-4-44-4-444-24-4-442222-2-2-200000000-2-2220000000000000000000000000000000000000000

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