Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (C19⋊C3)⋊#10596874 |
| derived, Hall | C72×C19 ⋊ C32×C4 |
| Hall | C19⋊C3×#3861 ⋊ C4 |
| Hall | C7⋊Dic133 ⋊ C32 |
| Sylow | C72 ⋊ C3×(C19⋊C3)⋊C4 |
| Sylow | C19 ⋊ C3×#10596874 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C19⋊C3)⋊#64424 |
| commutator, hypocenter | C72×C19 | C32×C4 |
| Fitting, socle, cosocle | C2×C72×C19 | C2×C32 |
| prime radical | C2×C19⋊C3×#3861 | C2 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C2 | |
360 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3724 |
Polycyclic presentation:
2,3^2,7^2,19,2|a^2=g,d^a=d^6,e^a=e^6,f^a=f^18,f^b=f^7,d^c=d^2,e^c=e^2198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 533);