Finite Group Databasebeta

← Group #72267883

Character table — Group #72267883

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size111133334444666666661212121212121212242424242424242424242424242464646464646464646464646464646464
order1222222222224444444444444444444444444444443366666666666666
χ11111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ3111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ411111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1111-1-1-1-1
χ511111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ611111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ722-2-22-22-222-2-20000000022-2-222-2-200000000000000-1-111-111-1-111-111-1-1
χ822-2-22-22-222-2-20000000022-2-222-2-2000000000000001+i321−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32
χ922-2-22-22-222-2-20000000022-2-222-2-2000000000000001−i321+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32
χ1022-2-22-22-2-2-2220000000022-2-2-2-22200000000000000-1-111-1-1-11111-1-1-111
χ1122-2-22-22-2-2-2220000000022-2-2-2-222000000000000001+i321−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32
χ1222-2-22-22-2-2-2220000000022-2-2-2-222000000000000001−i321+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32
χ132-22-222-2-22-22-22222-2-2-2-2000000002-2000000000000-1-11-111-11-11-111-11-1
χ142-22-222-2-22-22-22222-2-2-2-2000000002-20000000000001+i321−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32
χ152-22-222-2-22-22-22222-2-2-2-2000000002-20000000000001−i321+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32
χ162-22-222-2-2-22-222222-2-2-2-200000000-22000000000000-1-11-11-11-111-11-11-11
χ172-22-222-2-2-22-222222-2-2-2-200000000-220000000000001+i321−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32
χ182-22-222-2-2-22-222222-2-2-2-200000000-220000000000001−i321+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32
χ1933333333333333333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20333333333333-1-1-1-1-1-1-1-133333333-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ21333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-133-1-1-1-10000000000000000
χ22333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-133-1-10000000000000000
χ23333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1330000000000000000
χ2433333333-3-3-3-333333333-1-1-1-11111-3-3-1-1-1-1-1-11111110000000000000000
χ2533333333-3-3-3-3-1-1-1-1-1-1-1-13333-3-3-3-311-1-1-1-1-1-11111110000000000000000
χ2633333333-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-111111133-1-1-1-1-3-311110000000000000000
χ2733333333-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-1111111-1-133-1-111-3-3110000000000000000
χ2833333333-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1331111-3-30000000000000000
χ294-4-444-4-444-4-44000000000000000000000000000000111-1-11-1-111-1-11-1-11
χ304-4-444-4-444-4-44000000000000000000000000000000−1−i32−1+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32
χ314-4-444-4-444-4-44000000000000000000000000000000−1+i32−1−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32
χ324-4-444-4-44-444-4000000000000000000000000000000111-1-1-111-11-1-1-111-1
χ334-4-444-4-44-444-4000000000000000000000000000000−1−i32−1+i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32
χ344-4-444-4-44-444-4000000000000000000000000000000−1+i32−1−i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32
χ356666-2-2-2-200006-2-2-26-2-2-22-22-20000002-22-22-20000000000000000000000
χ366666-2-2-2-200006-2-2-26-2-2-2-22-22000000-22-22-220000000000000000000000
χ376666-2-2-2-20000-26-2-2-26-2-22-22-20000002-2-22-220000000000000000000000
χ386666-2-2-2-20000-26-2-2-26-2-2-22-22000000-222-22-20000000000000000000000
χ396666-2-2-2-20000-2-26-2-2-26-22-22-2000000-222-2-220000000000000000000000
χ406666-2-2-2-20000-2-26-2-2-26-2-22-220000002-2-222-20000000000000000000000
χ416666-2-2-2-20000-2-2-26-2-2-262-22-2000000-22-222-20000000000000000000000
χ426666-2-2-2-20000-2-2-26-2-2-26-22-220000002-22-2-220000000000000000000000
χ4366-6-66-66-666-6-600000000-2-222-2-222000000000000000000000000000000
χ4466-6-66-66-6-6-66600000000-2-22222-2-2000000000000000000000000000000
χ456-66-666-6-66-66-6-2-2-2-2222200000000-220000000000000000000000000000
χ466-66-666-6-6-66-66-2-2-2-22222000000002-20000000000000000000000000000
χ476-66-6-2-22200006-2-2-2-622200002i−2i2i−2i000000002i−2i2i−2i2i−2i0000000000000000
χ486-66-6-2-22200006-2-2-2-62220000−2i2i−2i2i00000000−2i2i−2i2i−2i2i0000000000000000
χ496-66-6-2-2220000-26-2-22-62200002i−2i2i−2i000000002i−2i−2i2i−2i2i0000000000000000
χ506-66-6-2-2220000-26-2-22-6220000−2i2i−2i2i00000000−2i2i2i−2i2i−2i0000000000000000
χ516-66-6-2-2220000-2-26-222-6200002i−2i2i−2i00000000−2i2i2i−2i−2i2i0000000000000000
χ526-66-6-2-2220000-2-26-222-620000−2i2i−2i2i000000002i−2i−2i2i2i−2i0000000000000000
χ536-66-6-2-2220000-2-2-26222-600002i−2i2i−2i00000000−2i2i−2i2i2i−2i0000000000000000
χ546-66-6-2-2220000-2-2-26222-60000−2i2i−2i2i000000002i−2i2i−2i−2i2i0000000000000000
χ551212-12-12-44-440000000000004-4-440000000000000000000000000000000000
χ561212-12-12-44-44000000000000-444-40000000000000000000000000000000000
χ5712-12-1212-444-400000000000000004i−4i−4i4i000000000000000000000000000000
χ5812-12-1212-444-40000000000000000−4i4i4i−4i000000000000000000000000000000

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