Finite Group DatabasebetaFinite Group Databasebeta| order | 33708 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C53 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C53×D53 |
| unambiguous semidirect product | C53⋊(C22×C3×C53) |
| unambiguous semidirect product | (C2×C53)⋊(C2×C3×C53) |
| Fitting, socle | C2×C3×C532 ⋊ C2 |
| derived | C53 ⋊ C22×C3×C53 |
| Hall | C3×C532 ⋊ C22 |
| Sylow | C532 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C53 | D53 |
| commutator, cosocle, hypocenter | C53 | C22×C3×C53 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C532 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C3×C53 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 636 |
8904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33708, 44);