Finite Group DatabasebetaFinite Group Databasebeta| order | 2532 |
| isoclinism | isoclinic class of C211⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C22×C211⋊C3 |
| Fitting, socle, Hall | C22×C211 ⋊ C3 |
| derived, Sylow | C211 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C211⋊C3 |
| commutator, cosocle, hypocenter | C211 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C211 | C3 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C22 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 215 |
| transitive degree | μt(G) = 844 |
292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2532, 10);