Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C2×C4 |
| direct product | C23×#1473 |
| 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 ◁ C2×C42×C23 ◁ G | |
214 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 736 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,27,32,29,33,39,46)(26,31,36,44,34,45,47,55)(28,30,38,41,35,42,49,53)(37,40,51,52,48,43,50,54);(25,30)(26,34)(27,38)(31,43)(33,42)(36,50)(37,48)(39,49)(40,45)(44,55)(47,51)(52,54);(24,26,35,48)(25,31,42,43)(27,36,49,50)(28,37,29,34)(30,40,33,45)(32,44,53,54)(38,51,39,47)(41,52,46,55)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#8489, C23×#8490, C2×C23×#1473, … |
| maximal normal subgroup of | C23×#8489, C23×#8490, C2×C23×#1473, … |
| maximal quotient of | C23×#7666, C23×#7669, C23×#7672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 205);