Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3585 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#3586 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | C23×D4 |
| commutator, Frattini, cosocle | C4 | C25×C17 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×#41×C17 ◁ G | |
1412 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)(20,28)(21,25)(22,34)(23,26)(24,30)(27,36)(29,42)(31,41)(32,39)(33,46)(35,38)(37,44)(40,45)(43,49)(47,48);(18,20,23,31)(19,24,26,38)(21,29,32,43)(22,35,36,30)(25,37,39,48)(27,41,34,28)(33,47,45,44)(40,49,46,42);(18,21)(19,25)(20,29)(22,33)(23,32)(24,37)(26,39)(27,40)(28,42)(30,44)(31,43)(34,46)(35,47)(36,45)(38,48)(41,49);(21,32)(25,39)(29,43)(33,45)(37,48)(40,46)(42,49)(44,47);(19,26)(24,38)(25,39)(27,34)(28,41)(37,48)(40,46)(42,49)697 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2318);