Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#2064 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C23×C23 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ G | |
208 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 208 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) = 43 |
| transitive degree | μt(G) = 1472 |
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)(28,29,32,39,34,38,33,37)(30,36,40,35,31,42,41,43);(24,25)(26,27)(28,30,32,40,34,31,33,41)(29,35,37,36,38,43,39,42);(25,27)(28,31,34,30)(29,36,38,42)(32,40,33,41)(35,39,43,37)598 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#2064, C23×#23601, C23×#23603, … |
| maximal normal subgroup of | C2×C23×#2064, C23×#23601, C23×#23603, … |
| maximal quotient of | C23×#10588, C23×#10590, C23×#10592, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 796);