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×#2642 |
| 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 | |
416 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 416 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) = 51 |
| transitive degree | μt(G) = 2944 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27)(30,34)(32,35)(37,41)(42,44)(43,49)(50,51);(24,25,26,27)(28,29,31,33)(30,32,34,35)(36,37)(38,44)(39,43)(40,41)(42,46)(45,51)(47,50)(48,49);(24,25)(26,27)(28,30)(29,32)(31,34)(33,35)(36,38,40,46)(37,42,41,44)(39,47,48,45)(43,51,49,50);(36,39,40,48)(37,43,41,49)(38,45,46,47)(42,50,44,51)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#10095, C23×#10103, C23×#18441, … |
| maximal normal subgroup of | C23×#10095, C23×#10103, C23×#18441, … |
| maximal quotient of | C23×#14261, C23×#14274, C23×#14283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1374);