Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2221 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#2223 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #466 |
| commutator, Frattini, cosocle | C2×C8 | C23×C17 |
| prime radical | C17×#472 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C17×#131 ◁ G | |
144 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 60 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)(19,25)(20,31)(21,34)(22,23)(26,35)(27,42)(28,39)(29,38)(30,40)(32,47)(33,36)(37,43)(44,49)(45,48);(18,19,26,38,23,29,21,25,24,30,34,39,22,28,35,40)(20,27,41,49,31,43,32,37,33,44,46,42,36,45,47,48);(18,20)(19,27)(21,32)(22,36)(23,31)(24,33)(25,37)(26,41)(28,45)(29,43)(30,44)(34,46)(35,47)(38,49)(39,42)(40,48)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 955);