Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | D637⋊(C3⋊D3) |
| Fitting, derived, Hall | C32×C13×C49 ⋊ C22 |
| Hall | C13×C49 ⋊ C2×C3⋊D3 |
| Hall | C32×C49 ⋊ C2×D13 |
| Hall | C32×C13 ⋊ C2×D49 |
| Sylow | C49 ⋊ C3⋊D3×D13 |
| Sylow | C13 ⋊ C3⋊D3×D49 |
| Sylow | C32 ⋊ D13×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C13×C49 | C22 |
| Frattini | C7 | D91⋊(C3⋊D3) |
| socle | C32×C7×C13 | C2×D7 |
| LCS | G ▷ C32×C13×C49 | |
| UCS | C1 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5733 |
Polycyclic presentation:
2^2,3^2,7,13,7|e^7=g^6,e^a=e^6g,f^a=f^12,g^a=g^6,c^b=c^2,d^b=d^2,e^b=e^6g,g^b=g^61488 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 231);