Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C22×C4 |
| direct product | C23×#1965 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C2×C23×#127 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G | |
396 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 736 |
A minimal faithful permutation representation — 3 generators on 35 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)(28,29,31,34,32,33,35,30);(28,30,31,33,32,34,35,29);(24,25,26,27)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#8469, C23×#8472, C23×#9253, … |
| maximal normal subgroup of | C23×#8469, C23×#8472, C23×#9253, … |
| maximal quotient of | C23×#9649, C23×#9653, C23×#9685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 697);