Finite Group DatabasebetaFinite Group Databasebeta| order | 25524 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#15667778⋊C3 |
| unambiguous semidirect product | #15667778⋊C32 |
| unambiguous semidirect product | (C3×#15667778)⋊C3 |
| Fitting, socle | C3×C709 ⋊ C3×C4 |
| derived, Sylow | C709 ⋊ C32×C4 |
| Hall | C3×C709⋊C3 ⋊ C4 |
| Hall | #15667778 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #15667778⋊C3 |
| commutator, hypocenter | C709 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C709 | C3×C4 |
| prime radical | C3×D709⋊C3 | C2 |
| cosocle | D709 | C2×C32 |
| LCS | G ▷ C709 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2127 |
213 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25524, 30);