Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C23 · Schur multiplier (H2) = C25×C4 |
| direct product | C23×#2328 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C24 |
| commutator | C22 | C23×C4×C23 |
| Frattini, cosocle | C23 | C24×C23 |
| prime radical | C2×C23×#127 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ G | |
740 conjugacy classes of subgroups; only the 296 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 296 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,27)(28,29,31,30)(32,33,36,34)(35,38,39,37);(28,30,31,29)(33,34)(37,38);(24,25,26,27)(32,34,36,33)(35,38,39,37);(32,35,36,39)(33,37,34,38)1012 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#9101, C23×#9105, C23×#9295, … |
| maximal normal subgroup of | C23×#9101, C23×#9105, C23×#9295, … |
| maximal quotient of | C23×#13779, C23×#13785, C23×#13791, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1060);