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×#3524 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C17 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
1030 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)(27,28)(30,38)(32,34)(36,41);(26,27,31,28)(29,34,37,32)(30,33,38,35)(36,40,41,39);(18,19)(20,23)(21,22)(24,25)(26,28,31,27)(29,34,37,32)(30,35,38,33)(36,40,41,39);(26,29,31,37)(27,32,28,34)(30,36,38,41)(33,39,35,40);(18,20,21,24)(19,23,22,25)(26,30)(27,33)(28,35)(29,36)(31,38)(32,39)(34,40)(37,41)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2256);