Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#1279 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | D4 |
| commutator | C4 | C4×C8×C17 |
| Frattini, cosocle | C2×C42 | C22×C17 |
| socle, prime radical | C23×C17 | C22⋊C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ C2×C42×C17 ◁ G | |
208 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 208 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) = 37 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 2 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(23,27)(24,25)(28,29)(30,31,33,36,34,37,32,35);(19,21)(22,23,25,28,26,29,24,27)(31,35,37,36)952 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 11);