Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#21439556 |
| derived | C3×C72×C13 ⋊ C3×C4 |
| Hall | C3×C7×#63271 ⋊ C4 |
| Hall | C72×C13 ⋊ C3×Dic3 |
| Sylow | C72 ⋊ C3⋊(Dic13⋊C3) |
| Sylow | C13 ⋊ ΓL(1,𝔽8)×Dic21 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#16838480 |
| commutator, hypocenter | C3×C72×C13 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C72×C13 | C2×C3 |
| prime radical | C2×C3×C7×#63271 | C2 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 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) = 3276 |
Polycyclic presentation:
2,3^2,7^2,13,2|a^2=g,c^a=c^2,e^a=e^6,f^a=f^12,d^b=d^2,f^b=f^9708 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 751);