Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#1397 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C17 | C22 |
| commutator | C2 | C4×C16×C17 |
| Frattini, cosocle | C2×C16 | C22×C17 |
| socle, prime radical | C22×C17 | C2×C16 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C17 ◁ G | |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
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)(22,23,24,29,25,30,32,41,26,31,33,42,35,43,44,51,27,28,34,38,36,39,45,48,37,40,46,49,47,50,52,53);(18,19,20,21)(23,28)(29,38)(30,39)(31,40)(41,48)(42,49)(43,50)(51,53)1360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 129);