Finite Group Databasebeta

← Group #797

Character table — Group #797

Order 96.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size111111111111111122222222222222223333333333333333
order116816416816216816416816348244812482448648244812482448216816416816216816416816
χ1111111111111111111111111111111111111111111111111
χ21ζζ2ζ3iζ5ζ6ζ7-1−ζ−ζ2−ζ3−i−ζ5−ζ6−ζ71ζζ2ζ3iζ5ζ6ζ7-1−ζ−ζ2−ζ3−i−ζ5−ζ6−ζ71ζζ2ζ3iζ5ζ6ζ7-1−ζ−ζ2−ζ3−i−ζ5−ζ6−ζ7
χ31ζ2iζ6-1−ζ2−i−ζ61ζ2iζ6-1−ζ2−i−ζ61ζ2iζ6-1−ζ2−i−ζ61ζ2iζ6-1−ζ2−i−ζ61ζ2iζ6-1−ζ2−i−ζ61ζ2iζ6-1−ζ2−i−ζ6
χ41ζ3ζ6−ζ−i−ζ7ζ2ζ5-1−ζ3−ζ6ζiζ7−ζ2−ζ51ζ3ζ6−ζ−i−ζ7ζ2ζ5-1−ζ3−ζ6ζiζ7−ζ2−ζ51ζ3ζ6−ζ−i−ζ7ζ2ζ5-1−ζ3−ζ6ζiζ7−ζ2−ζ5
χ51i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i
χ61ζ5−ζ2−ζ7i−ζ−ζ6ζ3-1−ζ5ζ2ζ7−iζζ6−ζ31ζ5−ζ2−ζ7i−ζ−ζ6ζ3-1−ζ5ζ2ζ7−iζζ6−ζ31ζ5−ζ2−ζ7i−ζ−ζ6ζ3-1−ζ5ζ2ζ7−iζζ6−ζ3
χ71ζ6−iζ2-1−ζ6i−ζ21ζ6−iζ2-1−ζ6i−ζ21ζ6−iζ2-1−ζ6i−ζ21ζ6−iζ2-1−ζ6i−ζ21ζ6−iζ2-1−ζ6i−ζ21ζ6−iζ2-1−ζ6i−ζ2
χ81ζ7−ζ6ζ5−iζ3−ζ2ζ-1−ζ7ζ6−ζ5i−ζ3ζ2−ζ1ζ7−ζ6ζ5−iζ3−ζ2ζ-1−ζ7ζ6−ζ5i−ζ3ζ2−ζ1ζ7−ζ6ζ5−iζ3−ζ2ζ-1−ζ7ζ6−ζ5i−ζ3ζ2−ζ
χ91-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-1
χ101−ζζ2−ζ3i−ζ5ζ6−ζ7-1ζ−ζ2ζ3−iζ5−ζ6ζ71−ζζ2−ζ3i−ζ5ζ6−ζ7-1ζ−ζ2ζ3−iζ5−ζ6ζ71−ζζ2−ζ3i−ζ5ζ6−ζ7-1ζ−ζ2ζ3−iζ5−ζ6ζ7
χ111−ζ2i−ζ6-1ζ2−iζ61−ζ2i−ζ6-1ζ2−iζ61−ζ2i−ζ6-1ζ2−iζ61−ζ2i−ζ6-1ζ2−iζ61−ζ2i−ζ6-1ζ2−iζ61−ζ2i−ζ6-1ζ2−iζ6
χ121−ζ3ζ6ζ−iζ7ζ2−ζ5-1ζ3−ζ6−ζi−ζ7−ζ2ζ51−ζ3ζ6ζ−iζ7ζ2−ζ5-1ζ3−ζ6−ζi−ζ7−ζ2ζ51−ζ3ζ6ζ−iζ7ζ2−ζ5-1ζ3−ζ6−ζi−ζ7−ζ2ζ5
χ131−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i
χ141−ζ5−ζ2ζ7iζ−ζ6−ζ3-1ζ5ζ2−ζ7−i−ζζ6ζ31−ζ5−ζ2ζ7iζ−ζ6−ζ3-1ζ5ζ2−ζ7−i−ζζ6ζ31−ζ5−ζ2ζ7iζ−ζ6−ζ3-1ζ5ζ2−ζ7−i−ζζ6ζ3
χ151−ζ6−i−ζ2-1ζ6iζ21−ζ6−i−ζ2-1ζ6iζ21−ζ6−i−ζ2-1ζ6iζ21−ζ6−i−ζ2-1ζ6iζ21−ζ6−i−ζ2-1ζ6iζ21−ζ6−i−ζ2-1ζ6iζ2
χ161−ζ7−ζ6−ζ5−i−ζ3−ζ2−ζ-1ζ7ζ6ζ5iζ3ζ2ζ1−ζ7−ζ6−ζ5−i−ζ3−ζ2−ζ-1ζ7ζ6ζ5iζ3ζ2ζ1−ζ7−ζ6−ζ5−i−ζ3−ζ2−ζ-1ζ7ζ6ζ5iζ3ζ2ζ
χ1711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ181ζζ2ζ3iζ5ζ6ζ7-1−ζ−ζ2−ζ3−i−ζ5−ζ6−ζ71ζζ2ζ3iζ5ζ6ζ7-1−ζ−ζ2−ζ3−i−ζ5−ζ6−ζ7-1−ζ−ζ2−ζ3−i−ζ5−ζ6−ζ71ζζ2ζ3iζ5ζ6ζ7
χ191ζ2iζ6-1−ζ2−i−ζ61ζ2iζ6-1−ζ2−i−ζ61ζ2iζ6-1−ζ2−i−ζ61ζ2iζ6-1−ζ2−i−ζ6-1−ζ2−i−ζ61ζ2iζ6-1−ζ2−i−ζ61ζ2iζ6
χ201ζ3ζ6−ζ−i−ζ7ζ2ζ5-1−ζ3−ζ6ζiζ7−ζ2−ζ51ζ3ζ6−ζ−i−ζ7ζ2ζ5-1−ζ3−ζ6ζiζ7−ζ2−ζ5-1−ζ3−ζ6ζiζ7−ζ2−ζ51ζ3ζ6−ζ−i−ζ7ζ2ζ5
χ211i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i1i-1−i-1−i1i-1−i1i-1−i1i-1−i1i
χ221ζ5−ζ2−ζ7i−ζ−ζ6ζ3-1−ζ5ζ2ζ7−iζζ6−ζ31ζ5−ζ2−ζ7i−ζ−ζ6ζ3-1−ζ5ζ2ζ7−iζζ6−ζ3-1−ζ5ζ2ζ7−iζζ6−ζ31ζ5−ζ2−ζ7i−ζ−ζ6ζ3
χ231ζ6−iζ2-1−ζ6i−ζ21ζ6−iζ2-1−ζ6i−ζ21ζ6−iζ2-1−ζ6i−ζ21ζ6−iζ2-1−ζ6i−ζ2-1−ζ6i−ζ21ζ6−iζ2-1−ζ6i−ζ21ζ6−iζ2
χ241ζ7−ζ6ζ5−iζ3−ζ2ζ-1−ζ7ζ6−ζ5i−ζ3ζ2−ζ1ζ7−ζ6ζ5−iζ3−ζ2ζ-1−ζ7ζ6−ζ5i−ζ3ζ2−ζ-1−ζ7ζ6−ζ5i−ζ3ζ2−ζ1ζ7−ζ6ζ5−iζ3−ζ2ζ
χ251-11-11-11-11-11-11-11-11-11-11-11-11-11-11-11-1-11-11-11-11-11-11-11-11
χ261−ζζ2−ζ3i−ζ5ζ6−ζ7-1ζ−ζ2ζ3−iζ5−ζ6ζ71−ζζ2−ζ3i−ζ5ζ6−ζ7-1ζ−ζ2ζ3−iζ5−ζ6ζ7-1ζ−ζ2ζ3−iζ5−ζ6ζ71−ζζ2−ζ3i−ζ5ζ6−ζ7
χ271−ζ2i−ζ6-1ζ2−iζ61−ζ2i−ζ6-1ζ2−iζ61−ζ2i−ζ6-1ζ2−iζ61−ζ2i−ζ6-1ζ2−iζ6-1ζ2−iζ61−ζ2i−ζ6-1ζ2−iζ61−ζ2i−ζ6
χ281−ζ3ζ6ζ−iζ7ζ2−ζ5-1ζ3−ζ6−ζi−ζ7−ζ2ζ51−ζ3ζ6ζ−iζ7ζ2−ζ5-1ζ3−ζ6−ζi−ζ7−ζ2ζ5-1ζ3−ζ6−ζi−ζ7−ζ2ζ51−ζ3ζ6ζ−iζ7ζ2−ζ5
χ291−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i1−i-1i-1i1−i-1i1−i-1i1−i-1i1−i
χ301−ζ5−ζ2ζ7iζ−ζ6−ζ3-1ζ5ζ2−ζ7−i−ζζ6ζ31−ζ5−ζ2ζ7iζ−ζ6−ζ3-1ζ5ζ2−ζ7−i−ζζ6ζ3-1ζ5ζ2−ζ7−i−ζζ6ζ31−ζ5−ζ2ζ7iζ−ζ6−ζ3
χ311−ζ6−i−ζ2-1ζ6iζ21−ζ6−i−ζ2-1ζ6iζ21−ζ6−i−ζ2-1ζ6iζ21−ζ6−i−ζ2-1ζ6iζ2-1ζ6iζ21−ζ6−i−ζ2-1ζ6iζ21−ζ6−i−ζ2
χ321−ζ7−ζ6−ζ5−i−ζ3−ζ2−ζ-1ζ7ζ6ζ5iζ3ζ2ζ1−ζ7−ζ6−ζ5−i−ζ3−ζ2−ζ-1ζ7ζ6ζ5iζ3ζ2ζ-1ζ7ζ6ζ5iζ3ζ2ζ1−ζ7−ζ6−ζ5−i−ζ3−ζ2−ζ
χ332222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ3422ζ2ζ22ζ32i2ζ52ζ62ζ7-2−2ζ−2ζ2−2ζ3−2i−2ζ5−2ζ6−2ζ7-1−ζ−ζ2−ζ3−i−ζ5−ζ6−ζ71ζζ2ζ3iζ5ζ6ζ70000000000000000
χ3522ζ22i2ζ6-2−2ζ2−2i−2ζ622ζ22i2ζ6-2−2ζ2−2i−2ζ6-1−ζ2−i−ζ61ζ2iζ6-1−ζ2−i−ζ61ζ2iζ60000000000000000
χ3622ζ32ζ6−2ζ−2i−2ζ72ζ22ζ5-2−2ζ3−2ζ62ζ2i2ζ7−2ζ2−2ζ5-1−ζ3−ζ6ζiζ7−ζ2−ζ51ζ3ζ6−ζ−i−ζ7ζ2ζ50000000000000000
χ3722i-2−2i22i-2−2i22i-2−2i22i-2−2i-1−i1i-1−i1i-1−i1i-1−i1i0000000000000000
χ3822ζ5−2ζ2−2ζ72i−2ζ−2ζ62ζ3-2−2ζ52ζ22ζ7−2i2ζ2ζ6−2ζ3-1−ζ5ζ2ζ7−iζζ6−ζ31ζ5−ζ2−ζ7i−ζ−ζ6ζ30000000000000000
χ3922ζ6−2i2ζ2-2−2ζ62i−2ζ222ζ6−2i2ζ2-2−2ζ62i−2ζ2-1−ζ6i−ζ21ζ6−iζ2-1−ζ6i−ζ21ζ6−iζ20000000000000000
χ4022ζ7−2ζ62ζ5−2i2ζ3−2ζ22ζ-2−2ζ72ζ6−2ζ52i−2ζ32ζ2−2ζ-1−ζ7ζ6−ζ5i−ζ3ζ2−ζ1ζ7−ζ6ζ5−iζ3−ζ2ζ0000000000000000
χ412-22-22-22-22-22-22-22-2-11-11-11-11-11-11-11-110000000000000000
χ422−2ζ2ζ2−2ζ32i−2ζ52ζ6−2ζ7-22ζ−2ζ22ζ3−2i2ζ5−2ζ62ζ7-1ζ−ζ2ζ3−iζ5−ζ6ζ71−ζζ2−ζ3i−ζ5ζ6−ζ70000000000000000
χ432−2ζ22i−2ζ6-22ζ2−2i2ζ62−2ζ22i−2ζ6-22ζ2−2i2ζ6-1ζ2−iζ61−ζ2i−ζ6-1ζ2−iζ61−ζ2i−ζ60000000000000000
χ442−2ζ32ζ62ζ−2i2ζ72ζ2−2ζ5-22ζ3−2ζ6−2ζ2i−2ζ7−2ζ22ζ5-1ζ3−ζ6−ζi−ζ7−ζ2ζ51−ζ3ζ6ζ−iζ7ζ2−ζ50000000000000000
χ452−2i-22i2−2i-22i2−2i-22i2−2i-22i-1i1−i-1i1−i-1i1−i-1i1−i0000000000000000
χ462−2ζ5−2ζ22ζ72i2ζ−2ζ6−2ζ3-22ζ52ζ2−2ζ7−2i−2ζ2ζ62ζ3-1ζ5ζ2−ζ7−i−ζζ6ζ31−ζ5−ζ2ζ7iζ−ζ6−ζ30000000000000000
χ472−2ζ6−2i−2ζ2-22ζ62i2ζ22−2ζ6−2i−2ζ2-22ζ62i2ζ2-1ζ6iζ21−ζ6−i−ζ2-1ζ6iζ21−ζ6−i−ζ20000000000000000
χ482−2ζ7−2ζ6−2ζ5−2i−2ζ3−2ζ2−2ζ-22ζ72ζ62ζ52i2ζ32ζ22ζ-1ζ7ζ6ζ5iζ3ζ2ζ1−ζ7−ζ6−ζ5−i−ζ3−ζ2−ζ0000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.