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×C4 |
| direct product | C23×#2660 |
| 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 | |
448 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 232 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)(28,29)(30,32)(31,33)(34,35)(36,37,40,38)(39,42,43,41);(24,25,26,27)(28,29,31,33)(30,32,35,34)(36,38,40,37)(39,41,43,42);(24,25)(26,27)(28,29)(30,34)(31,33)(32,35)(36,39,40,43)(37,41,38,42);(28,30,31,35)(29,32,33,34)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#10091, C23×#10093, C23×#10099, … |
| maximal normal subgroup of | C23×#10091, C23×#10093, C23×#10099, … |
| maximal quotient of | C23×#14276, C23×#14277, C23×#14282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1392);