Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2081 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#2082 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #397 |
| commutator, Frattini, cosocle | C22×C4 | C23×C17 |
| prime radical | C23×C17 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
184 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 184 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) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,28,24,29,22,27)(20,30,33,25,34,41,32,42)(21,35,37,43,38,44,39,26)(31,46,47,49,36,40,48,45);(18,20,24,34)(19,25,29,42)(21,36,38,31)(22,33,23,32)(26,40,43,46)(27,41,28,30)(35,49,44,45)(37,47,39,48);(18,21,22,37,24,38,23,39)(19,26,27,35,29,43,28,44)(20,31,32,47,34,36,33,48)(25,40,30,45,42,46,41,49)391 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 814);