Finite Group DatabasebetaFinite Group Databasebeta| order | 30464 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3145728 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C8 |
| abelian | C2×C7×C8×C16×C17 |
| multiplicative | (ℤ/46443)ˣ, (ℤ/48603)ˣ, (ℤ/60992)ˣ, (ℤ/61924)ˣ, (ℤ/64804)ˣ, (ℤ/92886)ˣ, (ℤ/97206)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4×C8 | C23×C7×C17 |
| socle, prime radical | C23×C7×C17 | C4×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
796 conjugacy classes of subgroups.
30464 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.