Finite Group DatabasebetaFinite Group Databasebeta| order | 25545 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×C131⋊C5 |
| unambiguous semidirect product | (C3×C13×C131)⋊C5 |
| Fitting, socle, Hall | C3×C13×C131 ⋊ C5 |
| derived, Sylow | C131 ⋊ C3×C5×C13 |
| Hall | C13×C131 ⋊ C3×C5 |
| Hall | C3×C131 ⋊ C5×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | C131⋊C5 |
| commutator, cosocle, hypocenter | C131 | C3×C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C131 | C5 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C3×C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5109 |
1209 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25545, 3);