Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#2634 |
| 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 192 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 192 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)(29,32)(33,35)(36,37,41,39)(38,44,46,42)(40,43,48,47)(45,50,51,49);(25,27)(29,32)(33,35)(36,38,41,46)(37,42,39,44)(40,45,48,51)(43,49,47,50);(24,25)(26,27)(28,29)(30,33)(31,32)(34,35)(36,39,41,37)(38,42,46,44)(40,43,48,47)(45,50,51,49);(28,30,31,34)(29,33,32,35)(36,40)(37,43)(38,45)(39,47)(41,48)(42,49)(44,50)(46,51)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#9190, C23×#10021, C23×#10025, … |
| maximal normal subgroup of | C23×#9190, C23×#10021, C23×#10025, … |
| maximal quotient of | C23×#14270, C23×#14289, C23×#14298, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1366);