Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#2024 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C23 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C2×C42×C23 ◁ G | |
290 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 108 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) = 2944 |
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)(28,29,31,33)(30,34,35,32)(37,40)(38,42)(41,43);(24,25)(26,27)(28,30,31,35)(29,32,33,34);(25,27)(36,37,39,41)(38,43,42,40)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7753, C23×#7755, C23×#7759, … |
| maximal normal subgroup of | C23×#7753, C23×#7755, C23×#7759, … |
| maximal quotient of | C23×#10341, C23×#10343, C23×#10349, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 756);