Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#30660660 |
| Fitting, socle | C2×C72×C19 ⋊ C2×C32 |
| derived, Hall | C72×C19 ⋊ C22×C32 |
| Hall | #3861⋊(C19⋊C3) ⋊ C22 |
| Hall | C2×C7⋊D133 ⋊ C32 |
| Sylow | C72 ⋊ C2×C3×D19⋊C3 |
| Sylow | C19 ⋊ C2×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #30660660 |
| commutator, cosocle, hypocenter | C72×C19 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C19 | C2×C32 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C2 | |
280 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 798 |
A minimal faithful permutation representation — 2 generators on 35 points:
(3,4,5,9,6,8)(11,14,15,12,13,16)(17,18)(19,21)(20,28)(22,24)(23,29)(25,27)(26,34)(30,31)(32,33);(1,2)(4,6,8)(5,7,9)(10,11,13,16,15,14,12)(18,20,23)(19,22,24)(21,26,27)(25,30,32)(28,31,35)(29,34,33)166 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 947);