Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#1648 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C17 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C17 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ G | |
194 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 72 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)(19,23)(20,21)(24,25)(26,27,32,36)(28,37,29,40)(30,35,31,34)(33,39,41,38);(18,19)(20,23)(21,25)(22,24)(26,28,32,29)(27,33,36,41)(30,39,31,38)(34,40,35,37);(18,20,22,21)(19,23,24,25)(26,29,32,28)(27,33,36,41)(30,38,31,39)(34,40,35,37)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 380);