Finite Group DatabasebetaFinite Group Databasebeta| order | 30130 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D131⋊C5 |
| unambiguous semidirect product | D131⋊(C5×C23) |
| unambiguous semidirect product | (C131⋊C5)⋊(C2×C23) |
| unambiguous semidirect product | (C23×D131)⋊C5 |
| Fitting, socle, Hall | C23×C131 ⋊ C2×C5 |
| derived, Sylow | C131 ⋊ C2×C5×C23 |
| Hall | C23×C131⋊C5 ⋊ C2 |
| Hall | C23×D131 ⋊ C5 |
| Hall | C131⋊C5 ⋊ C2×C23 |
| Hall | D131 ⋊ C5×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D131⋊C5 |
| commutator, cosocle, hypocenter | C131 | C2×C5×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C131 | C2×C5 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C23 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3013 |
529 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30130, 10);