Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#2049 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #394 |
| commutator, Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C2×#41×C23 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C22×C4×C23 ◁ G | |
254 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 80 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)(24,25,30,35)(26,36,39,51)(27,40,44,49)(28,34,29,33)(31,45,47,38)(32,42,50,43)(37,48,41,46)(52,55,54,53);(24,26)(25,31)(27,41)(28,45)(29,38)(30,39)(32,48)(33,51)(34,36)(35,47)(37,44)(40,54)(42,53)(43,55)(46,50)(49,52);(24,27,28,42,30,44,29,43)(25,32,33,49,35,50,34,40)(26,37,38,53,39,41,45,55)(31,46,36,52,47,48,51,54)529 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#2049, C23×#23525, C23×#24295, … |
| maximal normal subgroup of | C2×C23×#2049, C23×#23525, C23×#24295, … |
| maximal quotient of | C23×#10444, C23×#10445, C23×#10446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 781);