Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | ΓL(1,𝔽8)⋊C4×#87705 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C4×#87705) |
| derived, Hall | C72×C19 ⋊ C32×C4 |
| Hall | ΓL(1,𝔽8)×#87705 ⋊ C4 |
| Hall | C7×C19×Dic7 ⋊ C32 |
| Hall | C7×Dic7 ⋊ C3×C19⋊C3 |
| Sylow | C72 ⋊ C3×C4×C19⋊C3 |
| Sylow | C19 ⋊ ΓL(1,𝔽8)×ΓL(1,𝔽8)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽7)×#87705 |
| commutator, hypocenter | C72×C19 | C32×C4 |
| Fitting, socle, cosocle | C2×C72×C19 | C2×C32 |
| prime radical | C2×ΓL(1,𝔽8)×#87705 | C2 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C2 | |
152 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1596 |
658 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 561);