Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊#21439672 |
| Fitting, socle | C3×C72×C13 ⋊ Dic3 |
| derived, Hall | C3×C13×#3862 ⋊ C4 |
| Hall | C72×C13 ⋊ C3⋊Dic3 |
| Hall | C3×#3862 ⋊ #261 |
| Sylow | C72 ⋊ C3⋊(C3⋊#261) |
| Sylow | C13 ⋊ C3⋊#10596868 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C3×C13×#3862 | C4 |
| Fitting, socle | C3×C72×C13 | Dic3 |
| prime radical, cosocle | C3×D13×#3862 | C2 |
| LCS | G ▷ C3×C13×#3862 | |
| UCS | C1 | |
120 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 546 |
Polycyclic presentation:
2^2,3^2,13,7^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^5,f^a=f^4g,g^a=f^6g^3,e^b=e^12,f^c=f^2g^6,g^c=g^4249 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 1077);