Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#3515 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C17 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
1014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(23,25)(26,27,31,32)(28,29,33,36)(30,38,39,34)(35,41,40,37);(27,32)(29,36)(34,38)(37,41);(18,19)(20,23)(21,22)(24,25)(26,28,31,33)(27,29,32,36)(30,35,39,40)(34,37,38,41);(26,29)(27,33)(28,32)(30,37)(31,36)(34,40)(35,38)(39,41);(18,20,21,24)(19,23,22,25)(26,30)(27,34)(28,35)(29,37)(31,39)(32,38)(33,40)(36,41)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2247);