Finite Group DatabasebetaFinite Group Databasebeta| order | 33212 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C19 |
| direct product | C23×C19⋊Dic19 |
| unambiguous semidirect product | C19⋊(C23×Dic19) |
| derived, Sylow | C192 ⋊ C4×C23 |
| Hall | C192×C23 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | C19⋊D19 |
| commutator, hypocenter | C192 | C4×C23 |
| Frattini | C2 | C23×C19⋊D19 |
| Fitting, socle, prime radical | C2×C192×C23 | C2 |
| cosocle | C2×C192 | C2×C23 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C2×C23 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33212 |
8372 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33212, 12);