Finite Group DatabasebetaFinite Group Databasebeta| order | 23564 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×#10587739 |
| Fitting, socle, Hall | C43×C137 ⋊ C4 |
| derived, Sylow | C137 ⋊ C4×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | #10587739 |
| commutator, hypocenter | C137 | C4×C43 |
| Frattini | C1 | G |
| Fitting, socle | C43×C137 | C4 |
| prime radical | C43×D137 | C2 |
| cosocle | D137 | C2×C43 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C43 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5891 |
1634 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23564, 6);