Finite Group DatabasebetaFinite Group Databasebeta| order | 33411 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×#11744748 |
| Fitting, socle, Hall | C7×C37×C43 ⋊ C3 |
| derived, Hall | C7×C43 ⋊ C3×C37 |
| Hall | C37×C43 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C37 ⋊ C43⋊C3 |
| Sylow | C43 ⋊ ΓL(1,𝔽8)×C37 |
| Sylow | C7 ⋊ C37×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | #11744748 |
| commutator, cosocle, hypocenter | C7×C43 | C3×C37 |
| Frattini | C1 | G |
| Fitting, socle | C7×C37×C43 | C3 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C37 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11137 |
3811 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33411, 9);