Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1304 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#1308 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #95 |
| commutator | C23 | C42×C17 |
| Frattini, cosocle | C2×C42 | C22×C17 |
| prime radical | C23×C17 | C42 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 2 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,26,23,25,22,27)(20,28,29,33,30,24,31,32)(34,35,37,40,38,41,45,48)(36,42,44,49,43,39,46,47);(18,20,22,29,23,30,21,31)(19,24,27,32,25,28,26,33)(34,36)(35,39,41,42)(37,44)(38,43)(40,47,48,49)(45,46)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 40);