Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, derived | C3×C72×C13 ⋊ C22×C3 |
| Hall | C3×#14274262 ⋊ C22 |
| Hall | C72×C13 ⋊ C2×C3×D3 |
| Sylow | C72 ⋊ C2×C3⋊(D13⋊C3) |
| Sylow | C13 ⋊ D3×#64423 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C13 | C22×C3 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 | |
230 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 546 |
A minimal faithful permutation representation — 2 generators on 30 points:
(1,2,8)(3,9,13)(4,6,11)(5,12,7)(14,15,16)(18,22,21,19,20,23)(25,26,27)(28,30,29);(2,3)(4,6)(5,9)(7,8)(10,12)(11,13)(15,16)(17,18,21,22,20,23,19)(24,25,27,29,26,28,30)Polycyclic presentation:
2^2,3^2,7^2,13|d^a=d^2,g^a=g^12,e^b=e^6,e^c=e^4,f^c=f^4,g^c=g^3261 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 1233);