Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, Hall | C72×C13 ⋊ C2×C3×D3 |
| derived | C13×#3862 ⋊ C22×C3 |
| Hall | #19153212 ⋊ C22 |
| Sylow | C72 ⋊ C2×D3×C13⋊C3 |
| Sylow | C13 ⋊ (#64418⋊C2)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C13×#3862 | C22×C3 |
| Fitting, socle | C72×C13 | C2×C3×D3 |
| LCS | G ▷ C13×#3862 | |
| UCS | C1 | |
152 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 182 |
Polycyclic presentation:
2^2,3^2,13,7^2|d^a=d^2,f^a=g^5,g^a=f^3,d^b=d^2,f^b=g^2,g^b=f^4,e^c=e^3,f^c=f^2,g^c=g^2,f^d=f^4,g^d=g^2101 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 791);