Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C25×C4 |
| direct product | C23×#3027 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | C2×#120 |
| commutator, Frattini, cosocle | C23 | C24×C23 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C22×C4×C23 ◁ G | |
772 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 368 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(27,34)(29,35)(30,37)(32,38);(24,25)(26,29)(27,30)(28,31)(32,36)(33,35)(34,37)(38,39);(24,26)(25,29)(27,32)(28,33)(30,36)(31,35)(34,38)(37,39);(24,27,28,34)(25,30,31,37)(26,32,33,38)(29,36,35,39)667 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#13350, C23×#13351, C23×#13353, … |
| maximal normal subgroup of | C23×#13350, C23×#13351, C23×#13353, … |
| maximal quotient of | C23×#18300, C23×#18301, C23×#18302, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1759);