Finite Group DatabasebetaFinite Group Databasebeta| order | 23532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C53 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C37×C53 ⋊ C2×C3 |
| derived, Sylow | C37 ⋊ C22×C3×C53 |
| Hall | C2×C53×D37 ⋊ C3 |
| Hall | C53×C37⋊C3 ⋊ C22 |
| Hall | C37×C53 ⋊ C22×C3 |
| Hall | C2×D37 ⋊ C3×C53 |
| Hall | C37⋊C3 ⋊ C22×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C53 | D37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C22×C3×C53 |
| Frattini | C1 | G |
| Fitting, socle | C2×C37×C53 | C2×C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C53 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3922 |
1272 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23532, 21);