Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3008 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#3013 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×#41×C17 ◁ G | |
712 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)(24,31)(25,29)(26,34)(27,30)(28,32)(33,36)(35,37);(22,24,27,33)(23,28,30,37)(25,32,26,35)(29,36,34,31);(19,21)(22,23)(24,28)(25,34)(26,29)(27,30)(31,32)(33,37)(35,36);(22,25,27,26)(23,29,30,34)(24,32,33,35)(28,36,37,31)544 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1745);