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×#3556 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C17 |
| prime radical | C23×C17 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
890 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,21)(20,26,28,24)(22,29,30,25)(27,31,33,32)(34,35,39,43)(36,41,37,40)(38,46,47,42)(44,48,45,49);(18,20,23,28)(19,24,21,26)(22,27,30,33)(25,31,29,32)(34,35)(36,41)(37,40)(38,42)(39,43)(44,49)(45,48)(46,47);(34,36,39,37)(35,40,43,41)(38,44,47,45)(42,48,46,49);(18,21,23,19)(20,24,28,26)(22,29,30,25)(27,31,33,32)(34,37,39,36)(35,41,43,40)(38,45,47,44)(42,49,46,48);(18,22,23,30)(19,25,21,29)(20,27,28,33)(24,31,26,32)(34,38,39,47)(35,42,43,46)(36,44,37,45)(40,48,41,49)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2288);