Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#3276 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C17 |
| prime radical | C17×#547 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×D4×C17 ◁ G | |
472 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 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)(22,23,27,25)(24,30,33,37)(26,35,36,29)(28,31,34,32);(22,24,27,33)(23,28,25,34)(26,31,36,32)(29,37,35,30);(19,21)(22,25,27,23)(24,28,33,34)(26,35,36,29)(30,31,37,32);(24,31)(26,36)(28,37)(29,35)(30,34)(32,33)493 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2008);