Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1902 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#1904 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #386 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C2×C23×AGL(1,ℤ/8) | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C22×C4×C23 ◁ G | |
346 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 368 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,28,31,29,33,27,32)(26,34,36,38,37,39,35,30);(24,26)(25,30,33,38)(27,35)(28,36)(29,37)(31,34,32,39);(25,31)(27,28)(30,34)(32,33)(35,36)(38,39)667 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#1904, C23×#20998, C23×#22284, … |
| maximal normal subgroup of | C2×C23×#1904, C23×#20998, C23×#22284, … |
| maximal quotient of | C23×#9087, C23×#9089, C23×#9091, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 636);