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×#3563 |
| 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 | |
912 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)(20,27)(21,24)(22,30)(23,26)(25,31)(28,32)(29,33)(34,35,40,43)(36,38,41,37)(39,47,48,42)(44,45,49,46);(18,20,23,21)(19,24,26,27)(22,28,31,29)(25,32,30,33)(34,36,40,41)(35,37,43,38)(39,44,48,49)(42,45,47,46);(18,21,23,20)(19,24,26,27)(22,29,31,28)(25,32,30,33)(34,37,40,38)(35,41,43,36)(39,45,48,46)(42,49,47,44);(18,19)(20,27)(21,24)(22,25)(23,26)(28,33)(29,32)(30,31)(34,38,40,37)(35,36,43,41)(39,46,48,45)(42,44,47,49);(18,22)(19,25)(20,28)(21,29)(23,31)(24,32)(26,30)(27,33)(34,39)(35,42)(36,44)(37,45)(38,46)(40,48)(41,49)(43,47)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2295);