Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C2×C42 |
| direct product | C23×#2835 |
| 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 | |
380 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 168 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)(25,28)(29,31)(32,33)(34,36)(35,37)(38,39)(40,41,44,46)(42,43,45,47);(26,30)(29,31)(32,33,35,37)(34,36,39,38)(40,42)(41,43)(44,45)(46,47);(24,25,27,28)(26,29,30,31)(32,34,35,39)(33,36,37,38)(40,43)(41,45)(42,46)(44,47);(24,26)(25,29)(27,30)(28,31)(32,33)(34,38)(35,37)(36,39)598 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#12139, C23×#12233, C2×C23×#2835, … |
| maximal normal subgroup of | C23×#12139, C23×#12233, C2×C23×#2835, … |
| maximal quotient of | C23×#14627, C23×#14635, C23×#14647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1567);