Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#30660717 |
| Fitting, socle | C2×C72×C19 ⋊ C2×C9 |
| derived, Hall | C72×C19 ⋊ C22×C9 |
| Hall | C7×#11924781 ⋊ C22 |
| Hall | C2×C7×D133 ⋊ C9 |
| Sylow | C72 ⋊ C2×AGL(1,𝔽19) |
| Sylow | C19 ⋊ C2×D7×C7⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #30660717 |
| commutator, hypocenter | C72×C19 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C19 | C2×C9 |
| prime radical | C2×C7×(C19⋊C3)⋊D7 | C3 |
| cosocle | C72×C19⋊C3 | C22×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C2 | |
128 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1596 |
248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 956);