Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#2859 |
| 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 | |
472 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 264 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2944 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,27)(30,33)(31,35)(36,37,41,40)(38,43,42,39);(28,29,32,34)(30,31,33,35)(36,38)(37,39)(40,43)(41,42);(24,25,26,27)(28,30,32,33)(29,31,34,35)(36,39,41,43)(37,42,40,38);(28,31)(29,33)(30,34)(32,35)(36,40,41,37)(38,43,42,39)1012 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7660, C23×#7663, C23×#7680, … |
| maximal normal subgroup of | C23×#7660, C23×#7663, C23×#7680, … |
| maximal quotient of | C23×#14687, C23×#14699, C23×#14707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1591);