Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#2608 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C23 |
| prime radical | C24×C23 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ G | |
428 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(32,33)(34,36)(35,38)(37,39)(40,41,44,43)(42,46,47,45);(25,28)(29,31)(33,34)(37,38)(42,47)(45,46);(24,25)(26,29)(27,28)(30,31)(32,34,36,33)(35,38,39,37)(40,42,44,47)(41,45,43,46);(24,26,27,30)(25,29,28,31)(32,35)(33,37)(34,38)(36,39)(40,43,44,41)(42,46,47,45)874 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#10388, C23×#10389, C2×C23×#2608, … |
| maximal normal subgroup of | C23×#10388, C23×#10389, C2×C23×#2608, … |
| maximal quotient of | C23×#13953, C23×#14092, C23×#14094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1340);