Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×Dic399 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽8)×Dic133) |
| derived | C3×C72×C19 ⋊ C3×C4 |
| Hall | C3×C7×C19×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C72×C19 ⋊ C3×Dic3 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ Dic19 |
| Sylow | C72 ⋊ C3×Dic57 |
| Sylow | C19 ⋊ ΓL(1,𝔽8)×Dic21 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | ΓL(1,𝔽8)×D399 |
| commutator, hypocenter | C3×C72×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72×C19 | C2×C3 |
| prime radical | C2×C3×C7×C19×ΓL(1,𝔽8) | C2 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4788 |
2010 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 743);