Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1462 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C25 |
| direct product | C23×#1784 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C24×C23 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C23×C4×C23 ◁ G | |
564 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 144 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)(28,29,31,35,32,34,40,42)(30,36,37,43,38,33,39,41);(28,30,32,38)(29,33,34,36)(31,39,40,37)(35,43,42,41);(25,27)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7308, C23×#7315, C23×#7317, … |
| maximal normal subgroup of | C23×#7308, C23×#7315, C23×#7317, … |
| maximal quotient of | C23×#8299, C23×#8303, C23×#8306, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 516);