Finite Group DatabasebetaFinite Group Databasebeta| order | 29302 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×D299 |
| unambiguous semidirect product | C13⋊(C72×D23) |
| unambiguous semidirect product | C23⋊(C72×D13) |
| Fitting, socle, Hall | C72×C13×C23 ⋊ C2 |
| derived, Hall | C13×C23 ⋊ C2×C72 |
| Hall | C72×C23 ⋊ D13 |
| Hall | C72×C13 ⋊ D23 |
| Sylow | C23 ⋊ C72×D13 |
| Sylow | C13 ⋊ C72×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D299 |
| commutator, cosocle, hypocenter | C13×C23 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C13×C23 | C2 |
| LCS | G ▷ C13×C23 | |
| UCS | C1 ◁ C72 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14651 |
7399 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29302, 12);