Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17×C32 · Schur multiplier (H2) = C22 |
| direct product | C17×C22⋊C32 |
| unambiguous semidirect product | C22⋊(C17×C32) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C17 | C22 |
| commutator | C2 | C2×C17×C32 |
| Frattini, cosocle | C2×C16 | C22×C17 |
| socle | C22×C17 | C2×C16 |
| prime radical | C23×C17 | C16 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C17 ◁ G | |
82 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 2 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,24,28,25,29,32,38,26,30,33,39,35,41,44,48,27,31,34,40,36,42,45,49,37,43,46,50,47,51,52,53);(19,21)1360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 131);