Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#1492 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | C2×D4 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C42 | C23×C23 |
| socle | C22×C23 | C2×C22⋊C4 |
| prime radical | C23×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C2×C42×C23 ◁ G | |
276 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 112 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 — 3 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)(24,25)(26,28)(27,30)(29,31)(32,33,35,38,36,34,39,37);(25,28)(26,31)(29,30)(32,34)(33,36)(35,37)(38,39);(33,34)(37,38)1012 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#8353, C23×#8354, C23×#8357, … |
| maximal normal subgroup of | C23×#8353, C23×#8354, C23×#8357, … |
| maximal quotient of | C23×#7658, C23×#7659, C23×#7660, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 224);