Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#1629 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C23 |
| prime radical | D42×C23 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C42×C23 ◁ G | |
314 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 76 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) = 736 |
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)(24,25,27,30)(26,28,31,29)(32,33,36,39)(34,37,35,38);(25,28)(26,31)(29,30)(33,37)(34,35)(38,39);(33,38)(34,35)(37,39)598 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7517, C23×#13674, C2×C23×#1629, … |
| maximal normal subgroup of | C23×#7517, C23×#13674, C2×C23×#1629, … |
| maximal quotient of | C23×#7750, C23×#7754, C23×#7778, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 361);