Finite Group DatabasebetaFinite Group Databasebeta| order | 25652 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C112 · Schur multiplier (H2) = C11 |
| direct product | C112×#6157 |
| Fitting, socle, Hall | C112×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C4×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C112 | #6157 |
| commutator, hypocenter | C53 | C4×C112 |
| Frattini | C1 | G |
| Fitting, socle | C112×C53 | C4 |
| prime radical | C112×D53 | C2 |
| cosocle | D53 | C2×C112 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C112 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6413 |
2057 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25652, 22);