Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊(D13⋊C3))⋊D49 |
| unambiguous semidirect product | ((C13⋊C3)⋊D49)⋊D3 |
| Fitting, derived | C3×C13×C49 ⋊ C22×C3 |
| Hall | C3×C13⋊C3×C49 ⋊ C22 |
| Hall | C13×C49 ⋊ C2×C3×D3 |
| Hall | C3×C13⋊C3 ⋊ C2×D49 |
| Sylow | C49 ⋊ D3×D13⋊C3 |
| Sylow | C13 ⋊ C3×D3×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C13×C49 | C22×C3 |
| Frattini | C7 | (C3⋊(D13⋊C3))⋊D7 |
| socle | C3×C7×C13 | C2×C3×D7 |
| LCS | G ▷ C3×C13×C49 | |
| UCS | C1 | |
132 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1911 |
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,d^b=d^2,e^b=e^6g,g^b=g^6,f^c=f^3384 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 174);