Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C2×C43 |
| direct product | C23×#2819 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ G | |
580 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 580 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) = 43 |
| transitive degree | μt(G) = 1472 |
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)(28,29,31,33)(30,32,34,35)(36,37,40,39)(38,41,42,43);(25,27)(30,34)(32,35)(37,39)(38,42);(24,25)(26,27)(28,29)(30,32)(31,33)(34,35)(36,38)(37,41)(39,43)(40,42);(28,30)(29,32)(31,34)(33,35)(36,39,40,37)(38,41,42,43)598 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#10078, C23×#10081, C23×#10085, … |
| maximal normal subgroup of | C23×#10078, C23×#10081, C23×#10085, … |
| maximal quotient of | C23×#14623, C23×#14625, C23×#14632, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1551);