Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#2822 |
| 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 | |
380 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 184 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)(29,30)(33,34)(36,37,41,43)(38,44,46,39)(40,42,50,51)(45,49,48,47);(25,27)(28,29,32,30)(31,33,35,34)(36,38,41,46)(37,39,43,44)(40,48,50,45)(42,49,51,47);(24,25)(26,27)(28,30,32,29)(31,33,35,34)(36,39)(37,38)(40,49)(41,44)(42,48)(43,46)(45,51)(47,50);(28,31,32,35)(29,33,30,34)(36,40,41,50)(37,42,43,51)(38,45,46,48)(39,47,44,49)598 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#10080, C23×#10084, C23×#10087, … |
| maximal normal subgroup of | C23×#10080, C23×#10084, C23×#10087, … |
| maximal quotient of | C23×#14629, C23×#14631, C23×#14634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1554);