Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#3560 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C17 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
1056 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 544 |
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)(20,24)(26,27)(28,31)(29,34)(30,35)(32,36)(33,38)(37,39)(40,41);(19,22)(23,25)(27,28)(29,36)(33,35)(37,41);(18,19)(20,23)(21,22)(24,25)(26,28,31,27)(29,34,36,32)(30,35,38,33)(37,40,41,39);(18,20,21,24)(19,23,22,25)(26,29)(27,32)(28,34)(30,37)(31,36)(33,39)(35,40)(38,41);(26,30)(27,33)(28,35)(29,37)(31,38)(32,39)(34,40)(36,41)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2292);