Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C22×C4 |
| direct product | C23×#2809 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C23 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ G | |
368 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 192 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) = 2944 |
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)(24,25)(26,30)(27,28)(29,31)(32,33,35,37)(34,38,39,36)(42,43)(45,46);(25,28)(26,31)(32,33,35,37)(34,36,39,38)(40,41,44,47)(42,45,43,46);(24,26)(25,29)(27,31)(28,30)(32,33)(34,36)(35,37)(38,39)(40,42,44,43)(41,45,47,46);(24,25)(26,29)(27,28)(30,31)(32,34,35,39)(33,36,37,38)(40,43,44,42)(41,46,47,45)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7743, C23×#7760, C23×#7771, … |
| maximal normal subgroup of | C23×#7743, C23×#7760, C23×#7771, … |
| maximal quotient of | C23×#14446, C23×#14464, C23×#14467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1541);