Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#2032 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #393 |
| commutator, Frattini, cosocle | C24 | C23×C23 |
| prime radical | C22×D4×C23 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C24×C23 ◁ G | |
278 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 368 |
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)(26,29)(27,34,36,30)(28,31)(32,39,35,37)(33,38);(24,26)(25,29)(27,35,36,32)(28,33)(30,37,34,39)(31,38);(24,27)(25,30)(26,32)(28,36)(29,37)(31,34)(33,35)(38,39)529 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#2032, C23×#23474, C23×#23996, … |
| maximal normal subgroup of | C2×C23×#2032, C23×#23474, C23×#23996, … |
| maximal quotient of | C23×#10374, C23×#10375, C23×#10376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 764);