Finite Group DatabasebetaFinite Group Databasebeta| order | 3632 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊Dic227 |
| Sylow | C227 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D227 |
| commutator | C2×C227 | C2×C4 |
| Fitting, prime radical | C23×C227 | C2 |
| socle, cosocle | C22×C227 | C22 |
| hypercenter | C23 | D227 |
| hypocenter | C227 | C22⋊C4 |
| LCS | G ▷ C2×C227 ▷ C227 | |
| UCS | C1 ◁ C22 ◁ C23 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1816 |
Polycyclic presentation:
2^4,227|a^2=d,b^a=bc,e^a=e^226914 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3632, 18);