Finite Group DatabasebetaFinite Group Databasebeta| order | 30225 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×#11925882⋊C5 |
| unambiguous semidirect product | #11925882⋊C52 |
| unambiguous semidirect product | (C5×#11925882)⋊C5 |
| Fitting, socle | C5×C13×C31 ⋊ C3×C5 |
| derived, Hall | C13×C31 ⋊ C3×C52 |
| Hall | C5×C13×ΓL(1,𝔽32) ⋊ C3 |
| Hall | #11925882 ⋊ C52 |
| Hall | C5×ΓL(1,𝔽32) ⋊ C13⋊C3 |
| Sylow | C31 ⋊ C52×C13⋊C3 |
| Sylow | C13 ⋊ C5×(C31⋊C3)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #11925882⋊C5 |
| commutator, cosocle, hypocenter | C13×C31 | C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C31 | C3×C5 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 ◁ C5 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2015 |
305 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30225, 14);