Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2010 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#2098 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #127 |
| commutator, Frattini, cosocle | C22×C4 | C23×C17 |
| socle | C2×C17 | #399 |
| prime radical | C2×#41×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ G | |
210 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 210 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) = 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)(18,19,22,27,23,28,24,38)(20,29,31,41,33,45,32,25)(21,34,36,44,37,26,39,43)(30,46,35,49,47,42,48,40);(18,20,24,31,23,33,22,32)(19,25,38,29,28,41,27,45)(21,35,39,47,37,48,36,30)(26,42,44,40,34,46,43,49);(18,21)(19,26)(20,30)(22,36)(23,37)(24,39)(25,40)(27,43)(28,34)(29,46)(31,35)(32,48)(33,47)(38,44)(41,49)(42,45)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 830);