Finite Group DatabasebetaFinite Group Databasebeta| order | 25305 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #19099463⋊C5 |
| Fitting, socle, derived, Hall | C7×C241 ⋊ C3×C5 |
| Hall | C7×C241⋊C5 ⋊ C3 |
| Hall | #19099463 ⋊ C5 |
| Hall | C241⋊C5 ⋊ ΓL(1,𝔽8) |
| Sylow | C241 ⋊ C5×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ (C241⋊C3)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C241 | C3×C5 |
| LCS | G ▷ C7×C241 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1687 |
Polycyclic presentation:
3,5,7,241|c^a=c^2,d^a=d^15,d^b=d^91137 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25305, 9);