Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C24 |
| direct product | C2×C17×#344 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22⋊C4 |
| commutator | C22 | C2×C42×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| socle | C22×C17 | #95 |
| prime radical | C24×C17 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
388 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35);(3,4)(5,11,12,8)(6,10)(7,9)(13,17,18,15)(14,16);(3,5,6,13,7,12,14,18)(4,8,10,15,9,11,16,17)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 475);