Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊Dic819 |
| unambiguous semidirect product | C9⋊(C7⋊Dic91) |
| derived, Hall | C72×C9×C13 ⋊ C4 |
| Hall | C72×C13 ⋊ Dic9 |
| Hall | C72×C9 ⋊ Dic13 |
| Hall | C9×C13 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ Dic117 |
| Sylow | C13 ⋊ C7⋊Dic63 |
| Sylow | C9 ⋊ C7⋊Dic91 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C7⋊D819 |
| commutator, hypocenter | C72×C9×C13 | C4 |
| Frattini | C2×C3 | C3⋊(C7⋊D91) |
| Fitting, cosocle | C2×C72×C9×C13 | C2 |
| socle, prime radical | C2×C3×C72×C13 | D3 |
| LCS | G ▷ C72×C9×C13 | |
| UCS | C1 ◁ C2 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22932 |
Polycyclic presentation:
2,3,7^2,13,2,3|a^2=f,b^3=g^2,b^a=b^2g,c^a=c^6,d^a=d^6,e^a=e^12,g^a=g^25736 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 343);