Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#1400 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | C22⋊C4 |
| commutator | C22 | C2×C16×C17 |
| Frattini, cosocle | C2×C16 | C22×C17 |
| socle | C2×C17 | C22⋊C16 |
| prime radical | C23×C17 | C16 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C2×C16×C17 ◁ G | |
74 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)(18,19,20,25,21,26,29,37,22,27,30,38,31,39,42,47,23,24,28,34,32,35,40,44,33,36,41,45,43,46,48,49);(19,24)(20,28)(26,35)(27,36)(29,40)(30,41)(39,46)(42,48)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 132);