Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C72×C13 ⋊ C4×C9 |
| Hall | C7×#11717941 ⋊ C4 |
| Hall | C13×C7⋊Dic7 ⋊ C9 |
| Hall | C7⋊Dic7 ⋊ C13⋊C9 |
| Sylow | C72 ⋊ C4×C13⋊C9 |
| Sylow | C13 ⋊ (C7⋊C9)⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | #16838470 |
| 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,c^a=c^6,d^a=d^6,c^b=c^2,e^b=e^3756 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 306);