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×#3555 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C17 |
| prime radical | C17×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
910 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)(18,19,23,26)(20,21,28,24)(22,30,31,25)(27,32,33,29)(34,35,38,41)(36,39,44,42)(37,45,46,40)(43,48,49,47);(18,20,23,28)(19,24,26,21)(22,27,31,33)(25,32,30,29)(34,35)(36,42)(37,40)(38,41)(39,44)(43,48)(45,46)(47,49);(18,21,23,24)(19,20,26,28)(22,29,31,32)(25,27,30,33);(18,20)(19,24)(21,26)(22,27)(23,28)(25,32)(29,30)(31,33)(34,36)(35,39)(37,43)(38,44)(40,47)(41,42)(45,48)(46,49);(18,22,23,31)(19,25,26,30)(20,27,28,33)(21,29,24,32)(34,37,38,46)(35,40,41,45)(36,43,44,49)(39,47,42,48)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2287);