Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#1946 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | C2×D4 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| socle | C22×C23 | C4×D4 |
| prime radical | C23×C23 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ C22×C8×C23 ◁ G | |
200 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 200 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) = 43 |
| transitive degree | μt(G) = 736 |
A minimal faithful permutation representation — 3 generators on 43 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)(26,27)(28,29,32,37,33,38,42,36)(30,34,31,40,39,35,41,43);(25,27)(28,30,32,31,33,39,42,41)(29,34,37,40,38,35,36,43);(28,31,32,39,33,41,42,30)(29,35,36,40,38,34,37,43)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7125, C23×#12944, C23×#12956, … |
| maximal normal subgroup of | C23×#7125, C23×#12944, C23×#12956, … |
| maximal quotient of | C23×#9595, C23×#9596, C23×#9597, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 678);