Finite Group DatabasebetaFinite Group Databasebeta| order | 25389 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C13×C31 ⋊ C32 |
| Hall | C13×C31 ⋊ C3×ΓL(1,𝔽8) |
| Hall | C7×C31 ⋊ C3×C13⋊C3 |
| Hall | C7×C13 ⋊ C3×C31⋊C3 |
| Sylow | C31 ⋊ ΓL(1,𝔽8)×C13⋊C3 |
| Sylow | C13 ⋊ ΓL(1,𝔽8)×C31⋊C3 |
| Sylow | C7 ⋊ C13⋊C3×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C13×C31 | C32 |
| LCS | G ▷ C7×C13×C31 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2821 |
Polycyclic presentation:
3^2,7,13,31|d^a=d^3,e^a=e^25,c^b=c^4,d^b=d^3365 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25389, 28);