Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | Dic13⋊#89205 |
| derived, Hall | C72×C13 ⋊ C4×C9 |
| Hall | C13⋊#89205 ⋊ C4 |
| Hall | C72×Dic13 ⋊ C9 |
| Hall | Dic13 ⋊ #89205 |
| Sylow | C72 ⋊ Dic13⋊C9 |
| Sylow | C13 ⋊ C4×#89205 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D13⋊#3862 |
| commutator, hypocenter | C72×C13 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C72×C13 | C2×C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C2×C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3276 |
Polycyclic presentation:
2,3,7^2,13,2,3|a^2=f,b^3=g,e^a=e^12,c^b=c^2,d^b=d^4,e^b=e^3816 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 312);