Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2002 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#2003 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #120 |
| 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 | |
382 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 382 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)(30,34)(31,33)(32,36)(35,39)(37,42)(38,43)(40,41);(29,33)(31,39)(34,42)(35,36)(37,40)(41,43);(25,27)(28,30,32,38)(29,34,36,43)(31,40,39,37)(33,41,35,42)598 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#2003, C23×#23399, C23×#23400, … |
| maximal normal subgroup of | C2×C23×#2003, C23×#23399, C23×#23400, … |
| maximal quotient of | C23×#9915, C23×#9921, C23×#9923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 735);