Finite Group Databasebeta

← Group #72340592

Character table — Group #72340592

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55
size1133666666666666888121212121212121212121212121212121212242424242424242464646464128128128128128128
order1222444444444444444222222224444444444444444443366121212121212
χ11111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ3111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ411111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-11-1111-1-1-111111-1-11-1-1
χ511111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-11-1111-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ611111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-11-1111-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ71111-1-1-1-11111-1-1-1-1-11-11111-1-1-1-111-1-1-1-11111-1111-11-1-11111-11-1-11-1
χ81111-1-1-1-11111-1-1-1-1-11-11111-1-1-1-111-1-1-1-11111-1111-11-1-1−1−i32−1+i32−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32
χ91111-1-1-1-11111-1-1-1-1-11-11111-1-1-1-111-1-1-1-11111-1111-11-1-1−1+i32−1−i32−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32
χ101111-1-1-1-1-1-1-1-11111-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11-1-11
χ111111-1-1-1-1-1-1-1-11111-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-111−1−i32−1+i32−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32
χ121111-1-1-1-1-1-1-1-11111-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-111−1+i32−1−i32−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32
χ133333111111113333-3-33-1-1-1-1-1-1-1-13311111111-3-3-1-111-1-10000000000
χ14333311111111-1-1-1-1-3-33-1-1-1-133-1-1-1-111-3-311-3-3113-111-1-10000000000
χ15333311111111-1-1-1-1-3-33-1-1-1-1-1-133-1-1-3-311-3-31111-1311-1-10000000000
χ163333111133331111-33-333-1-11111-1-11111-1-1-1-11-1-1-1-3-11-30000000000
χ1733331111-3-3-3-3-1-1-1-1-3-3333-1-1-1-1-1-1-1-11111111111-1-1-31-130000000000
χ1833331111-1-1-1-11111-33-3-1-1-1-111-3-3-1-1-3-31133-1-11-1-131-1110000000000
χ1933331111-1-1-1-11111-33-3-1-1-1-1-3-311-1-111-3-3-1-1331-13-11-1110000000000
χ2033331111-1-1-1-1-3-3-3-3-33-3-1-1-1-11111331111-1-1-1-1-33-1-11-1110000000000
χ2133333333111111113-3-3-1-1331111-1-1-1-1-1-11111-11-1-1-1-3-310000000000
χ2233333333-1-1-1-1-1-1-1-1333-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-10000000000
χ233333-3-3-3-31111-1-1-1-1-3-33-1-133-1-1-1-1-1-11111111111-1-11-33-10000000000
χ243333-3-3-3-3-1-1-1-11111-33-3-1-1331111-1-11111-1-1-1-11-1-1-113-310000000000
χ253333-1-1-1-1111111113-3-3-1-1-1-111-3-3-1-133-1-1-3-311-11-13-11110000000000
χ263333-1-1-1-1111111113-3-3-1-1-1-1-3-311-1-1-1-13311-3-3-113-1-11110000000000
χ273333-1-1-1-11111-3-3-3-33-3-3-1-1-1-1111133-1-1-1-111113-3-1-1-11110000000000
χ283333-1-1-1-13333-1-1-1-133333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13-1-130000000000
χ293333-1-1-1-1-3-3-3-311113-3-333-1-11111-1-1-1-1-1-11111-11-1-1311-30000000000
χ303333-1-1-1-1-1-1-1-13333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-133-1-1-1-1-1-10000000000
χ313333-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-133-1-1-1-1-1-133-1-133-1-13-1-1-1-1-10000000000
χ323333-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-133-1-133-1-133-1-1-1-1-13-1-1-1-10000000000
χ336-6-22004i−4i004i−4i004-40002-22-22-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000
χ346-6-22004i−4i00−4i4i00-440002-22-2-22-222-22i−2i2i−2i−2i2i−2i2i000000000000000000
χ356-6-22004i−4i4i−4i004-400000-222-22-2-22-22−2i2i−2i2i2i−2i−2i2i000000000000000000
χ366-6-22004i−4i−4i4i00-4400000-222-2-222-2-22−2i2i−2i2i−2i2i2i−2i000000000000000000
χ376-6-2200−4i4i004i−4i00-440002-22-2-22-222-2−2i2i−2i2i2i−2i2i−2i000000000000000000
χ386-6-2200−4i4i00−4i4i004-40002-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000
χ396-6-2200−4i4i4i−4i00-4400000-222-2-222-2-222i−2i2i−2i2i−2i−2i2i000000000000000000
χ406-6-2200−4i4i−4i4i004-400000-222-22-2-22-222i−2i2i−2i−2i2i2i−2i000000000000000000
χ416-6-224i−4i00004i−4i4-4000002-2-22-222-2-22−2i2i2i−2i−2i2i−2i2i000000000000000000
χ426-6-224i−4i0000−4i4i-44000002-2-222-2-22-22−2i2i2i−2i2i−2i2i−2i000000000000000000
χ436-6-224i−4i004i−4i00004-4000-22-22-22-222-22i−2i−2i2i−2i2i2i−2i000000000000000000
χ446-6-224i−4i00−4i4i0000-44000-22-222-22-22-22i−2i−2i2i2i−2i−2i2i000000000000000000
χ456-6-22−4i4i00004i−4i-44000002-2-222-2-22-222i−2i−2i2i−2i2i−2i2i000000000000000000
χ466-6-22−4i4i0000−4i4i4-4000002-2-22-222-2-222i−2i−2i2i2i−2i2i−2i000000000000000000
χ476-6-22−4i4i004i−4i0000-44000-22-222-22-22-2−2i2i2i−2i−2i2i2i−2i000000000000000000
χ486-6-22−4i4i00−4i4i00004-4000-22-22-22-222-2−2i2i2i−2i2i−2i−2i2i000000000000000000
χ498-88-80000000000000000000000000000000000000000022-2-2000000
χ508-88-800000000000000000000000000000000000000000−1−i3−1+i31+i31−i3000000
χ518-88-800000000000000000000000000000000000000000−1+i3−1−i31−i31+i3000000
χ521212-4-444-4-444-4-4-4-444000000000000000000000000000000000000000
χ531212-4-444-4-4-4-44444-4-4000000000000000000000000000000000000000
χ541212-4-4-4-44444-4-444-4-4000000000000000000000000000000000000000
χ551212-4-4-4-444-4-444-4-444000000000000000000000000000000000000000

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