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×#3568 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C17 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
958 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(18,19,23,25)(20,29,33,31)(21,24,28,34)(22,36,37,27)(26,40,39,30)(32,45,46,43)(35,47,42,38)(41,44,48,49);(19,25)(20,30)(21,28)(26,31)(27,36)(29,39)(32,44)(33,40)(35,42)(41,45)(43,48)(46,49);(18,20,23,33)(19,26,25,39)(21,31,28,29)(22,32,37,46)(24,30,34,40)(27,41,36,48)(35,45,42,43)(38,44,47,49);(18,21,34,19)(20,31,40,26)(22,35,47,27)(23,28,24,25)(29,30,39,33)(32,45,49,41)(36,37,42,38)(43,44,48,46);(18,22,34,47)(19,27,21,35)(20,32,40,49)(23,37,24,38)(25,36,28,42)(26,41,31,45)(29,43,39,48)(30,44,33,46)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2300);