Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2081 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#2082 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #397 |
| commutator, Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C23×C23 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C22×C4×C23 ◁ G | |
184 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 72 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 — 3 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)(24,25,29,34,30,35,28,33)(26,36,39,31,40,47,38,48)(27,41,43,49,44,50,45,32)(37,52,53,55,42,46,54,51);(24,26,30,40)(25,31,35,48)(27,42,44,37)(28,39,29,38)(32,46,49,52)(33,47,34,36)(41,55,50,51)(43,53,45,54);(24,27,28,43,30,44,29,45)(25,32,33,41,35,49,34,50)(26,37,38,53,40,42,39,54)(31,46,36,51,48,52,47,55)529 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#2082, C23×#23652, C23×#24987, … |
| maximal normal subgroup of | C2×C23×#2082, C23×#23652, C23×#24987, … |
| maximal quotient of | C23×#10632, C23×#10633, C23×#10635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 814);