Finite Group DatabasebetaFinite Group Databasebeta| order | 22925 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C25 · Schur multiplier (H2) = C1 |
| direct product | C7×C131⋊C25 |
| unambiguous semidirect product | C131⋊(C7×C25) |
| unambiguous semidirect product | (C7×C131)⋊C25 |
| derived, Sylow | C131 ⋊ C7×C25 |
| Hall | C7×C131 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | C131⋊C5 |
| commutator, hypocenter | C131 | C7×C25 |
| Frattini | C5 | C7×C131⋊C5 |
| Fitting, socle, prime radical | C5×C7×C131 | C5 |
| cosocle | C5×C131 | C5×C7 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C5×C7 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22925 |
1085 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22925, 2);