Finite Group DatabasebetaFinite Group Databasebeta| order | 30597 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×#10620253 |
| Fitting, socle, Hall | C7×C31×C47 ⋊ C3 |
| derived, Hall | C7×C31 ⋊ C3×C47 |
| Hall | C31×C47 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C47 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ ΓL(1,𝔽8)×C47 |
| Sylow | C7 ⋊ C47×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | #10620253 |
| commutator, cosocle, hypocenter | C7×C31 | C3×C47 |
| Frattini | C1 | G |
| Fitting, socle | C7×C31×C47 | C3 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C47 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10199 |
3525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30597, 4);