Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#1331 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | D8 |
| commutator | C8 | C2×C8×C17 |
| Frattini, cosocle | C4×C8 | C22×C17 |
| socle | C22×C17 | #102 |
| prime radical | C2×D8×C17 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C42×C17 ◁ C4×C8×C17 ◁ G | |
110 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 1088 |
A minimal faithful permutation representation — 2 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,22,21,23,24,25)(26,27)(28,31)(29,38)(30,34)(32,35)(33,36)(37,40)(39,41);(27,31)(28,35)(29,36)(32,33)(34,40)(37,41)(38,39)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 63);