Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C22 |
| direct product | C2×C17×#364 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | D4 |
| commutator | C4 | C22×C8×C17 |
| Frattini, cosocle | C2×C8 | C23×C17 |
| socle | C22×C17 | C4⋊C8 |
| prime radical | C23×C17 | M16 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C22×C8×C17 ◁ G | |
168 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35);(3,4,7,12,8,11,16,18,9,13,15,10,6,17,5,14);(3,5,6,15,9,16,8,7)(4,10,11,14,13,12,17,18)952 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 884);