Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#2612 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C17 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
388 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24)(21,22)(23,25)(34,35,38,41)(36,40,37,39);(19,22)(23,24)(26,27,29,31)(28,30,32,33)(34,36,38,37)(35,39,41,40);(18,19)(20,23)(21,22)(24,25)(26,27)(28,30)(29,31)(32,33)(34,37,38,36)(35,40,41,39);(18,20,21,25)(19,23,22,24)(26,28,29,32)(27,30,31,33)(34,35)(36,39)(37,40)(38,41)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1344);