Finite Group DatabasebetaFinite Group Databasebeta| order | 30667 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C337⋊C7 |
| unambiguous semidirect product | C337⋊(C7×C13) |
| unambiguous semidirect product | (C13×C337)⋊C7 |
| Fitting, socle, Hall | C13×C337 ⋊ C7 |
| derived, Sylow | C337 ⋊ C7×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C337⋊C7 |
| commutator, cosocle, hypocenter | C337 | C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C337 | C7 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C13 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4381 |
715 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30667, 1);