Finite Group Databasebeta

← Group #72340818

Character table — Group #72340818

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size11233666666612162424242424242424323248484848486464641123366666661216242424242424242432324848484848646464
order124224444444428888888836244886612224224444444428888888866244886612
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111
χ31111111111111-11111111111-1-1-1-1-1-1-111111111111111-11111111111-1-1-1-1-1-1-11
χ41111111111111-1-1-1-1-1-1-1-1-111-11111-1-111111111111111-1-1-1-1-1-1-1-1-111-11111-1-11
χ52222222222222200000000-1-120000-1-1-12222222222222200000000-1-120000-1-1-1
χ62222222222222-200000000-1-1-2000011-12222222222222-200000000-1-1-2000011-1
χ722-222222-2-2-22-2000000000220000000-222-222222-2-2-22-2000000000220000000-2
χ822-222222-2-2-22-2000000000-1-100000−i3i3122-222222-2-2-22-2000000000-1-100000−i3i31
χ922-222222-2-2-22-2000000000-1-100000i3−i3122-222222-2-2-22-2000000000-1-100000i3−i31
χ102-202-222-2000-200−i2i2−i2−i2−i2i2i2i22-2000000002-202-222-2000-200−i2i2−i2−i2−i2i2i2i22-200000000
χ112-202-222-2000-200i2−i2i2i2i2−i2−i2−i22-2000000002-202-222-2000-200i2−i2i2i2i2−i2−i2−i22-200000000
χ1233333-1-1-13-1-1-1-13111-1-11-1-100-111-1-100033333-1-1-13-1-1-1-13111-1-11-1-100-111-1-1000
χ1333333-1-1-13-1-1-1-13-1-1-111-11100-1-1-11100033333-1-1-13-1-1-1-13-1-1-111-11100-1-1-111000
χ1433333-1-1-13-1-1-1-1-3111-1-11-1-1001-1-11100033333-1-1-13-1-1-1-1-3111-1-11-1-1001-1-111000
χ1533333-1-1-13-1-1-1-1-3-1-1-111-11100111-1-100033333-1-1-13-1-1-1-1-3-1-1-111-11100111-1-1000
χ164-404-444-4000-40000000000-22000000004-404-444-4000-40000000000-2200000000
χ17666-2-22-22-222-2-20000000000002-200000666-2-22-22-222-2-20000000000002-200000
χ18666-2-22-22-222-2-2000000000000-2200000666-2-22-22-222-2-2000000000000-2200000
χ19666-2-2-22-2-2-2-222022-200-2000000000000666-2-2-22-2-2-2-222022-200-2000000000000
χ20666-2-2-22-2-2-2-2220-2-22002000000000000666-2-2-22-2-2-2-2220-2-22002000000000000
χ2166-666-2-2-2-622-22000000000000000000066-666-2-2-2-622-220000000000000000000
χ2266-6-2-22-222-2-2-22000000000000002i−2i00066-6-2-22-222-2-2-22000000000000002i−2i000
χ2366-6-2-22-222-2-2-2200000000000000−2i2i00066-6-2-22-222-2-2-2200000000000000−2i2i000
χ2466-6-2-2-22-22222-200002-202-2000000000066-6-2-2-22-22222-200002-202-20000000000
χ2566-6-2-2-22-22222-20000-220-22000000000066-6-2-2-22-22222-20000-220-220000000000
χ266-606-6-2-22000200−i2i2−i2i2i2i2−i2−i200000000006-606-6-2-22000200−i2i2−i2i2i2i2−i2−i20000000000
χ276-606-6-2-22000200i2−i2i2−i2−i2−i2i2i200000000006-606-6-2-22000200i2−i2i2−i2−i2−i2i2i20000000000
χ286-60-22-22204-4-200−i2i2i2−i2i2−i2i2−i200000000006-60-22-22204-4-200−i2i2i2−i2i2−i2i2−i20000000000
χ296-60-22-22204-4-200i2−i2−i2i2−i2i2−i2i200000000006-60-22-22204-4-200i2−i2−i2i2−i2i2−i2i20000000000
χ306-60-22-2220-44-200−i2i2i2i2−i2−i2−i2i200000000006-60-22-2220-44-200−i2i2i2i2−i2−i2−i2i20000000000
χ316-60-22-2220-44-200i2−i2−i2−i2i2i2i2−i200000000006-60-22-2220-44-200i2−i2−i2−i2i2i2i2−i20000000000
χ3212-120-444-4-400040000000000000000000012-120-444-4-4000400000000000000000000
χ3311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3411111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-1
χ351111111111111-11111111111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111111-1
χ361111111111111-1-1-1-1-1-1-1-1-111-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-111-1
χ372222222222222200000000-1-120000-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000011-20000111
χ382222222222222-200000000-1-1-2000011-1-2-2-2-2-2-2-2-2-2-2-2-2-22000000001120000-1-11
χ3922-222222-2-2-22-2000000000220000000-2-2-22-2-2-2-2-2222-22000000000-2-200000002
χ4022-222222-2-2-22-2000000000-1-100000−i3i31-2-22-2-2-2-2-2222-220000000001100000i3−i3-1
χ4122-222222-2-2-22-2000000000-1-100000i3−i31-2-22-2-2-2-2-2222-220000000001100000−i3i3-1
χ422-202-222-2000-200−i2i2−i2−i2−i2i2i2i22-200000000-220-22-2-22000200i2−i2i2i2i2−i2−i2−i2-2200000000
χ432-202-222-2000-200i2−i2i2i2i2−i2−i2−i22-200000000-220-22-2-22000200−i2i2−i2−i2−i2i2i2i2-2200000000
χ4433333-1-1-13-1-1-1-13111-1-11-1-100-111-1-1000-3-3-3-3-3111-31111-3-1-1-111-111001-1-111000
χ4533333-1-1-13-1-1-1-13-1-1-111-11100-1-1-111000-3-3-3-3-3111-31111-3111-1-11-1-100111-1-1000
χ4633333-1-1-13-1-1-1-1-3111-1-11-1-1001-1-111000-3-3-3-3-3111-311113-1-1-111-11100-111-1-1000
χ4733333-1-1-13-1-1-1-1-3-1-1-111-11100111-1-1000-3-3-3-3-3111-311113111-1-11-1-100-1-1-111000
χ484-404-444-4000-40000000000-2200000000-440-44-4-44000400000000002-200000000
χ49666-2-22-22-222-2-20000000000002-200000-6-6-622-22-22-2-222000000000000-2200000
χ50666-2-22-22-222-2-2000000000000-2200000-6-6-622-22-22-2-2220000000000002-200000
χ51666-2-2-22-2-2-2-222022-200-2000000000000-6-6-6222-22222-2-20-2-22002000000000000
χ52666-2-2-22-2-2-2-2220-2-22002000000000000-6-6-6222-22222-2-2022-200-2000000000000
χ5366-666-2-2-2-622-220000000000000000000-6-66-6-62226-2-22-20000000000000000000
χ5466-6-2-22-222-2-2-22000000000000002i−2i000-6-6622-22-2-2222-200000000000000−2i2i000
χ5566-6-2-22-222-2-2-2200000000000000−2i2i000-6-6622-22-2-2222-2000000000000002i−2i000
χ5666-6-2-2-22-22222-200002-202-20000000000-6-66222-22-2-2-2-220000-220-220000000000
χ5766-6-2-2-22-22222-20000-220-220000000000-6-66222-22-2-2-2-2200002-202-20000000000
χ586-606-6-2-22000200−i2i2−i2i2i2i2−i2−i20000000000-660-6622-2000-200i2−i2i2−i2−i2−i2i2i20000000000
χ596-606-6-2-22000200i2−i2i2−i2−i2−i2i2i20000000000-660-6622-2000-200−i2i2−i2i2i2i2−i2−i20000000000
χ606-60-22-22204-4-200−i2i2i2−i2i2−i2i2−i20000000000-6602-22-2-20-44200i2−i2−i2i2−i2i2−i2i20000000000
χ616-60-22-22204-4-200i2−i2−i2i2−i2i2−i2i20000000000-6602-22-2-20-44200−i2i2i2−i2i2−i2i2−i20000000000
χ626-60-22-2220-44-200−i2i2i2i2−i2−i2−i2i20000000000-6602-22-2-204-4200i2−i2−i2−i2i2i2i2−i20000000000
χ636-60-22-2220-44-200i2−i2−i2−i2i2i2i2−i20000000000-6602-22-2-204-4200−i2i2i2i2−i2−i2−i2i20000000000
χ6412-120-444-4-4000400000000000000000000-121204-4-444000-400000000000000000000

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