Finite Group DatabasebetaFinite Group Databasebeta| order | 22716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #19150945⋊C4 |
| derived, Sylow | C631 ⋊ C4×C9 |
| Hall | #19150945 ⋊ C4 |
| Hall | Dic631 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #19150945⋊C2 |
| commutator, hypocenter | C631 | C4×C9 |
| Fitting, socle | C2×C631 | C2×C9 |
| prime radical, cosocle | C2×C631⋊C3 | C2×C3 |
| LCS | G ▷ C631 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2524 |
Polycyclic presentation:
2,3^2,631,2|a^2=e,b^3=c,d^a=d^630,d^b=d^376,d^c=d^43106 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22716, 17);