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×#3010 |
| 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 | |
732 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 544 |
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)(23,27)(25,32)(28,34)(29,33)(31,36)(35,37);(22,23,26,29)(24,28,30,35)(25,33,32,27)(31,37,36,34);(19,21)(22,24)(23,28)(25,31)(26,30)(27,34)(29,35)(32,36)(33,37);(24,30)(28,35)(31,36)(34,37)544 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1742);