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×#3565 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C17 |
| 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)(18,19,22,23)(20,26,27,24)(21,29,30,25)(28,31,33,32)(34,35)(36,41)(37,42)(38,46)(39,40)(43,47)(44,45)(48,49);(19,23)(20,27)(25,29)(28,33)(35,40)(37,41)(43,46)(45,48);(18,20,22,27)(19,24,23,26)(21,28,30,33)(25,31,29,32)(34,36,39,42)(35,41,40,37)(38,44,47,49)(43,48,46,45);(18,19)(20,24)(21,25)(22,23)(26,27)(28,31)(29,30)(32,33)(34,37,39,41)(35,42,40,36)(38,45,47,48)(43,49,46,44);(18,21,22,30)(19,25,23,29)(20,28,27,33)(24,31,26,32)(34,38,39,47)(35,43,40,46)(36,44,42,49)(37,45,41,48)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2297);