Finite Group DatabasebetaFinite Group Databasebeta| order | 33212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D23×D361 |
| unambiguous semidirect product | (C23×D361)⋊C2 |
| unambiguous semidirect product | (D23×C361)⋊C2 |
| unambiguous semidirect product | D8303⋊C2 |
| Fitting, derived, Hall | C23×C361 ⋊ C22 |
| Sylow | C361 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D361 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C23×C361 | C22 |
| Frattini | C19 | D19×D23 |
| socle | C19×C23 | C2×D19 |
| LCS | G ▷ C23×C361 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8303 |
2366 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33212, 6);