Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#2864 |
| 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 | |
400 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)(18,19,21,23)(20,22,24,25)(27,29)(31,32)(34,35,38,41)(36,40,37,39);(18,19)(20,22)(21,23)(24,25)(26,27,30,29)(28,31,33,32)(34,36,38,37)(35,39,41,40);(18,19)(20,22)(21,23)(24,25)(26,28,30,33)(27,31,29,32)(34,35)(36,39)(37,40)(38,41);(18,20,21,24)(19,22,23,25)(26,29,30,27)(28,32,33,31)(34,37,38,36)(35,40,41,39)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1596);