Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #365 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#1385 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #106 |
| commutator | C8 | C42×C17 |
| Frattini, cosocle | C22×C8 | C22×C17 |
| socle | C2×C17 | #340 |
| prime radical | C23×C17 | Q16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C22×C8×C17 ◁ G | |
124 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(18,19,22,28,25,30,24,40)(20,31,33,46,35,47,38,42)(21,29,23,39,37,45,36,27)(26,34,41,32,44,48,43,49);(18,20,23,34,22,38,37,49,25,35,36,48,24,33,21,32)(19,26,29,42,40,41,27,31,30,44,45,46,28,43,39,47)544 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 117);