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×#3557 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C17 |
| prime radical | C17×#540 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
930 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)(20,25)(21,26)(22,30)(23,24)(27,31)(28,29)(32,33)(35,39)(36,42)(37,45)(47,49);(19,24)(21,25)(27,30)(29,32)(34,35,38,39)(36,43,42,40)(37,41,45,46)(44,49,48,47);(18,20,23,26)(19,25,24,21)(22,28,31,33)(27,32,30,29)(34,35)(36,40)(37,41)(38,39)(42,43)(44,47)(45,46)(48,49);(18,21,23,25)(19,26,24,20)(22,29,31,32)(27,33,30,28)(34,36,38,42)(35,40,39,43)(37,44,45,48)(41,47,46,49);(18,22,23,31)(19,27,24,30)(20,28,26,33)(21,29,25,32)(34,37,38,45)(35,41,39,46)(36,44,42,48)(40,47,43,49)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2289);