Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#1370 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | D4 |
| commutator | C4 | C2×C16×C17 |
| Frattini, cosocle | C4×C8 | C22×C17 |
| socle, prime radical | C22×C17 | C4⋊C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C4×C8×C17 ◁ G | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
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)(19,22)(20,23)(24,25)(26,27,28,31,29,32,34,37,30,33,35,38,36,39,40,41);(18,19,23,25,21,24,20,22)952 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 102);