Finite Group DatabasebetaFinite Group Databasebeta| order | 25506 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C2×C3×#16862572 |
| Fitting, socle | C2×C3×C13×C109 ⋊ C3 |
| derived, Hall | C13×C109 ⋊ C2×C32 |
| Hall | C2×C13×C109 ⋊ C32 |
| Hall | C2×C109 ⋊ C3×C13⋊C3 |
| Sylow | C109 ⋊ C2×C3×C13⋊C3 |
| Hall | C2×C13 ⋊ C3×C109⋊C3 |
| Sylow | C13 ⋊ C2×C3×C109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #16862572 |
| commutator, cosocle, hypocenter | C13×C109 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C13×C109 | C3 |
| LCS | G ▷ C13×C109 | |
| UCS | C1 ◁ C2×C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8502 |
2850 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25506, 72);