Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1714 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C8 |
| direct product | C23×#1715 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #127 |
| commutator, Frattini, cosocle | C42 | C23×C23 |
| prime radical | C23×#493 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C42×C23 ◁ G | |
220 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 220 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) = 39 |
| transitive degree | μt(G) = 1472 |
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)(25,28)(26,29)(30,31)(33,36)(34,38)(37,39);(24,25,29,31,27,30,26,28);(25,30)(28,31)(32,33,34,36,35,37,38,39)598 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7533, C23×#12366, C2×C23×#1715, … |
| maximal normal subgroup of | C23×#7533, C23×#12366, C2×C23×#1715, … |
| maximal quotient of | C23×#8819, C23×#9827, C23×#9829, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 447);