Finite Group DatabasebetaFinite Group Databasebeta| order | 23270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D2327 |
| unambiguous semidirect product | C13⋊(C5×D179) |
| unambiguous semidirect product | C179⋊(C5×D13) |
| Fitting, socle, Hall | C5×C13×C179 ⋊ C2 |
| derived, Hall | C13×C179 ⋊ C2×C5 |
| Hall | C5×C179 ⋊ D13 |
| Sylow | C179 ⋊ C5×D13 |
| Hall | C5×C13 ⋊ D179 |
| Sylow | C13 ⋊ C5×D179 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D2327 |
| commutator, cosocle, hypocenter | C13×C179 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C179 | C2 |
| LCS | G ▷ C13×C179 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11635 |
5825 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23270, 4);