Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2021 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#2029 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #120 |
| commutator, Frattini, cosocle | C24 | C23×C23 |
| prime radical | C25×C23 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C24×C23 ◁ G | |
466 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 84 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)(24,25,27,30)(26,32,33,29)(28,31,35,37)(34,38,39,36);(24,26,27,33)(25,29,30,32)(28,34,35,39)(31,36,37,38);(29,36)(32,38)598 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7426, C23×#12202, C23×#12203, … |
| maximal normal subgroup of | C23×#7426, C23×#12202, C23×#12203, … |
| maximal quotient of | C23×#10340, C23×#10341, C23×#10344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 761);