Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#2019 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C2×C23×AGL(1,ℤ/8) | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ G | |
362 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 736 |
A minimal faithful permutation representation — 3 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)(24,25)(26,27)(28,29,32,36)(30,37,40,42)(31,34,41,35)(33,38,43,39);(25,27)(28,30)(29,33)(31,38)(32,40)(34,37)(35,42)(36,43)(39,41);(29,34)(30,38)(31,41)(35,36)(37,42)(39,40)598 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#2019, C23×#23438, C23×#23439, … |
| maximal normal subgroup of | C2×C23×#2019, C23×#23438, C23×#23439, … |
| maximal quotient of | C23×#9975, C23×#9978, C23×#9987, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 751);