Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#1392 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C23 | #99 |
| commutator | C23 | C42×C23 |
| Frattini, cosocle | C2×#41 | C22×C23 |
| socle | C2×C23 | #342 |
| prime radical | C2×#41×C23 | C22 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C23 ◁ C2×C4×C23 ◁ C2×#41×C23 ◁ G | |
158 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 736 |
A minimal faithful permutation representation — 2 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,28,33,30,35,29,34)(26,36,38,51,40,53,39,52)(27,41,42,50,43,32,44,48)(31,45,46,37,47,54,49,55);(24,26,29,39,30,40,28,38)(25,31,34,46,35,47,33,49)(27,37,42,54,43,55,44,45)(32,36,48,52,41,53,50,51)598 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7400, C23×#7401, C23×#7407, … |
| maximal normal subgroup of | C23×#7400, C23×#7401, C23×#7407, … |
| maximal quotient of | C23×#7188, C23×#7203, C23×#7216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 124);