Finite Group DatabasebetaFinite Group Databasebeta| order | 33708 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C532 · Schur multiplier (H2) = C2×C53 |
| direct product | A4×C532 |
| unambiguous semidirect product | C22⋊(C3×C532) |
| unambiguous semidirect product | (C22×C53)⋊(C3×C53) |
| Fitting, socle, Hall | C22×C532 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C532 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C532 | A4 |
| commutator, cosocle, hypocenter | C22 | C3×C532 |
| Frattini | C1 | G |
| Fitting, socle | C22×C532 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C532 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11236 |
11236 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33708, 42);