Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#2647 |
| 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 | |
360 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 360 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) = 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)(25,26)(29,30)(32,33)(34,37)(35,38)(36,39)(40,41,44,42)(43,46,47,45);(24,25,28,26)(27,29,31,30)(32,34)(33,35)(36,38)(37,39)(40,42,44,41)(43,45,47,46);(24,26,28,25)(27,29,31,30)(32,34)(33,37)(35,39)(36,38)(40,43,44,47)(41,45,42,46);(24,27,28,31)(25,29,26,30)(32,35,36,37)(33,38,39,34)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#29133, C23×#29134, C23×#29135, … |
| maximal normal subgroup of | C23×#29133, C23×#29134, C23×#29135, … |
| maximal quotient of | C23×#14266, C23×#14276, C23×#14277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1379);