Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C19 · Schur multiplier (H2) = C2×C3 |
| direct product | C19×ΓL(1,𝔽8)×C22⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | (C22×ΓL(1,𝔽8))⋊(C19×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×ΓL(1,𝔽8))⋊(A4×C19) |
| Fitting, socle, Hall | C22×C72×C19 ⋊ C32 |
| derived, Hall | C22×C72 ⋊ C32×C19 |
| Hall | C72×C19 ⋊ C3×A4 |
| Hall | C22×C19 ⋊ ΓL(1,𝔽8)2 |
| Sylow | C72 ⋊ C3×A4×C19 |
| Sylow | C22 ⋊ C19×ΓL(1,𝔽8)2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | ΓL(1,𝔽8)×C22⋊ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C22×C72 | C32×C19 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72×C19 | C32 |
| LCS | G ▷ C22×C72 | |
| UCS | C1 ◁ C19 | |
132 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1596 |
1140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 1295);