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×#1785 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C22×#41×C23 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C23×C4×C23 ◁ G | |
584 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 136 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)(28,29,32,37,33,36,31,35)(30,38,39,43,40,34,41,42);(28,30)(29,34)(31,39)(32,41)(33,40)(35,42)(36,38)(37,43);(25,27)(28,31,33,32)(29,35,36,37)(30,39,40,41)(34,42,38,43)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7306, C23×#7309, C23×#7312, … |
| maximal normal subgroup of | C23×#7306, C23×#7309, C23×#7312, … |
| maximal quotient of | C23×#8300, C23×#8301, C23×#8304, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 517);