Finite Group DatabasebetaFinite Group Databasebeta| order | 33708 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×#30682883 |
| Fitting, socle | C2×C532 ⋊ D3 |
| derived, Hall | C532⋊C3 ⋊ C22 |
| Sylow | C532 ⋊ C2×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #30682883 |
| commutator, cosocle, hypocenter | C532⋊C3 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C532 | D3 |
| LCS | G ▷ C532⋊C3 | |
| UCS | C1 ◁ C2 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 318 |
1098 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33708, 26);