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×#1653 |
| 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)(19,22)(20,24)(23,25)(26,27,31,35)(28,36,39,40)(29,32,30,34)(33,37,41,38);(18,19,21,23)(20,25,24,22)(27,32)(29,30)(33,40)(34,35)(36,41)(37,38);(26,28,31,39)(27,33,35,41)(29,38,30,37)(32,40,34,36)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 385);