Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×ΓL(1,𝔽8)×D399 |
| unambiguous semidirect product | (C2×C3)⋊(ΓL(1,𝔽8)×D133) |
| Fitting, socle | C2×C3×C72×C19 ⋊ C2×C3 |
| derived | C3×C72×C19 ⋊ C22×C3 |
| Hall | C3×C7×C19×ΓL(1,𝔽8) ⋊ C22 |
| Hall | C72×C19 ⋊ C2×C3×D3 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ C2×D19 |
| Sylow | C72 ⋊ C2×C3×D57 |
| Sylow | C19 ⋊ C2×ΓL(1,𝔽8)×D21 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | ΓL(1,𝔽8)×D399 |
| commutator, cosocle, hypocenter | C3×C72×C19 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C72×C19 | C2×C3 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 ◁ C2 | |
184 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 57 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, 1428);