Finite Group DatabasebetaFinite Group Databasebeta| order | 25172 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C31⋊(Dic29⋊C7) |
| unambiguous semidirect product | Dic899⋊C7 |
| derived, Hall | C29×C31 ⋊ C4×C7 |
| Hall | C31×C29⋊C7 ⋊ C4 |
| Hall | Dic899 ⋊ C7 |
| Hall | C29⋊C7 ⋊ Dic31 |
| Sylow | C31 ⋊ Dic29⋊C7 |
| Sylow | C29 ⋊ C7×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C31⋊(D29⋊C7) |
| commutator, hypocenter | C29×C31 | C4×C7 |
| Fitting, socle, cosocle | C2×C29×C31 | C2×C7 |
| prime radical | C2×C31×C29⋊C7 | C2 |
| LCS | G ▷ C29×C31 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3596 |
Polycyclic presentation:
2,7,29,31,2|a^2=e,c^a=c^28,d^a=d^30,c^b=c^16362 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25172, 12);