Finite Group DatabasebetaFinite Group Databasebeta| order | 25524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×D709⋊C9 |
| unambiguous semidirect product | D709⋊(C2×C9) |
| unambiguous semidirect product | (C2×D709)⋊C9 |
| unambiguous semidirect product | (C709⋊C9)⋊C22 |
| unambiguous semidirect product | (C2×C709⋊C9)⋊C2 |
| derived, Sylow | C709 ⋊ C22×C9 |
| Hall | C709⋊C9 ⋊ C22 |
| Hall | C2×D709 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D709⋊C3 |
| commutator, hypocenter | C709 | C22×C9 |
| Frattini | C3 | C2×D709⋊C3 |
| Fitting, socle | C2×C3×C709 | C2×C3 |
| prime radical | C2×C3×D709 | C3 |
| cosocle | C3×C709 | C22×C3 |
| LCS | G ▷ C709 | |
| UCS | C1 ◁ C2×C3 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12762 |
744 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25524, 9);