Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | D7×#4294⋊D7 |
| unambiguous semidirect product | (D7×#4294)⋊D7 |
| derived, Hall | C72×C19 ⋊ C22×C9 |
| Hall | C72×#4294 ⋊ C22 |
| Hall | D7×D133 ⋊ C9 |
| Hall | #4294 ⋊ D72 |
| Sylow | C72 ⋊ C2×#4294⋊C2 |
| Sylow | C19 ⋊ C9×D72 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D7×(C19⋊C3)⋊D7 |
| commutator, hypocenter | C72×C19 | C22×C9 |
| Fitting, socle, cosocle | C3×C72×C19 | C22×C3 |
| prime radical | C3×D7×D133 | C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C3 | |
156 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2394 |
540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 387);