Finite Group DatabasebetaFinite Group Databasebeta| order | 23852 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×#67063 |
| Fitting, socle, Hall | C67×C89 ⋊ C4 |
| derived, Sylow | C89 ⋊ C4×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | #67063 |
| commutator, hypocenter | C89 | C4×C67 |
| Frattini | C1 | G |
| Fitting, socle | C67×C89 | C4 |
| prime radical | C67×D89 | C2 |
| cosocle | D89 | C2×C67 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C67 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5963 |
1742 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23852, 6);