Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#1415 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D16 |
| commutator | C16 | C2×C4×C17 |
| Frattini, cosocle | C2×C16 | C22×C17 |
| prime radical | C2×C17×D16 | C2 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×C17 ◁ C2×C8×C17 ◁ 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)(25,37)(26,40)(27,32)(29,33)(30,34)(31,38)(35,47)(36,43)(39,53)(41,49)(42,48)(44,52)(45,50)(46,51);(23,28)(24,33)(25,34)(26,38)(29,30)(31,47)(32,43)(35,52)(36,50)(37,41)(39,51)(40,42)(44,53)(45,46)(48,49)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 147);