Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#2048 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #394 |
| commutator, Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C2×C23×AGL(1,ℤ/8) | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C22×C4×C23 ◁ G | |
274 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 80 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 — 3 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)(25,30)(26,33)(27,28)(31,38)(32,36)(34,35);(24,25)(26,31)(27,36)(28,30)(29,32)(33,37)(34,39)(35,38);(24,26,27,34,29,35,28,33)(25,31,30,37,32,38,36,39)529 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#2048, C23×#23525, C23×#24295, … |
| maximal normal subgroup of | C2×C23×#2048, C23×#23525, C23×#24295, … |
| maximal quotient of | C23×#10440, C23×#10441, C23×#10442, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 780);