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×#2817 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C23 |
| prime radical | C24×C23 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ G | |
444 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 444 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) = 1472 |
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)(40,43,49,47)(45,51,48,50);(25,27)(29,32)(30,34)(36,38,41,46)(37,42,39,44)(40,48,49,45)(43,51,47,50);(24,25)(26,27)(28,29)(30,33)(31,32)(34,35)(36,39,41,37)(38,42,46,44)(40,43,49,47)(45,51,48,50);(28,30)(29,33)(31,34)(32,35)(36,40,41,49)(37,43,39,47)(38,45,46,48)(42,50,44,51)598 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#9982, C23×#9985, C23×#12095, … |
| maximal normal subgroup of | C23×#9982, C23×#9985, C23×#12095, … |
| maximal quotient of | C23×#14626, C23×#14627, C23×#14629, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1549);