Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#2483 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C23 |
| prime radical | C25×C23 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ G | |
700 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 216 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 — 4 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)(25,27)(28,29,32,30)(31,34,35,33)(37,40)(38,42);(29,30)(33,34)(36,37)(38,41)(39,40)(42,43);(24,25)(26,27)(28,30,32,29)(31,34,35,33)(36,38,39,42)(37,41,40,43);(28,31)(29,33)(30,34)(32,35)(36,37)(38,41)(39,40)(42,43)874 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#9500, C23×#9502, C23×#10338, … |
| maximal normal subgroup of | C23×#9500, C23×#9502, C23×#10338, … |
| maximal quotient of | C23×#13869, C23×#13992, C23×#14040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1215);