Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C7 |
| unambiguous semidirect product | C3⋊(C3⋊(C7⋊Dic91)) |
| unambiguous semidirect product | C7⋊(C3⋊Dic273) |
| derived, Hall | C32×C72×C13 ⋊ C4 |
| Hall | C72×C13 ⋊ C3⋊Dic3 |
| Hall | C32×C72 ⋊ Dic13 |
| Hall | C32×C13 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ C3⋊Dic39 |
| Sylow | C13 ⋊ C3⋊(C3⋊(C7⋊Dic7)) |
| Sylow | C32 ⋊ C7⋊Dic91 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C3⋊(C7⋊D91)) |
| commutator, hypocenter | C32×C72×C13 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C32×C72×C13 | C2 |
| LCS | G ▷ C32×C72×C13 | |
| UCS | C1 ◁ C2 | |
360 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22932 |
Polycyclic presentation:
2,3^2,7^2,13,2|a^2=g,b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^6,f^a=f^125736 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 768);