Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1665 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#1680 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C17 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C17 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ G | |
150 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,24)(20,25,23,21)(26,27)(28,34)(29,31)(30,38)(32,36)(33,37)(35,41)(39,40);(18,20,21,19,22,23,25,24)(27,31)(32,40)(33,38)(34,41);(26,28,29,35)(27,32,31,40)(30,39,37,36)(33,41,38,34)493 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 412);