Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#26013839 |
| derived | C3×C72×C19 ⋊ C3×C4 |
| Hall | C3×C7×#87704 ⋊ C4 |
| Hall | C72×C19 ⋊ C3×Dic3 |
| Sylow | C72 ⋊ C3⋊((C19⋊C3)⋊C4) |
| Sylow | C19 ⋊ C3⋊(ΓL(1,𝔽8)⋊Dic7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#19150306 |
| commutator, hypocenter | C3×C72×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72×C19 | C2×C3 |
| prime radical | C2×C3×C7×#87704 | C2 |
| LCS | G ▷ C3×C72×C19 | |
| UCS | C1 ◁ C2 | |
136 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 136 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) = 4788 |
Polycyclic presentation:
2,3^2,7^2,19,2|a^2=g,c^a=c^2,d^a=d^6,e^a=e^6,f^a=f^18,d^b=d^2,f^b=f^7996 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 723);