Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| Fitting, derived, Hall | C13×C49 ⋊ C32×C4 |
| Hall | C13⋊C3×C49⋊C3 ⋊ C4 |
| Hall | C49⋊#261 ⋊ C32 |
| Sylow | C49 ⋊ C3×AGL(1,𝔽13) |
| Sylow | C13 ⋊ C3×(C49⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C13×C49 | C32×C4 |
| Frattini | C7 | ΓL(1,𝔽8)⋊AGL(1,𝔽13) |
| socle | C7×C13 | C3×ΓL(1,𝔽8)⋊C4 |
| prime radical | D13⋊C3×C49⋊C3 | C2 |
| cosocle | D13×C49 | C2×C32 |
| LCS | G ▷ C13×C49 | |
| UCS | C1 | |
108 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 637 |
Polycyclic presentation:
2,3^2,2,7,13,7|a^2=d,e^7=g^6,e^a=e^6g,f^a=f^5,g^a=g^6,f^b=f^3,e^c=e^2g^3,g^c=g^2,f^d=f^12103 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 126);