Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C2×C17×#421 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×D4 |
| commutator | C4 | C23×C4×C17 |
| Frattini, cosocle | C2×C4 | C24×C17 |
| socle | C22×C17 | C2×C22⋊C4 |
| prime radical | C22×#41×C17 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
772 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35);(3,4,7,10,8,11,6,15)(5,12,14,9,13,18,16,17);(3,5)(4,9)(6,16)(7,14)(8,13)(10,18)(11,17)(12,15);(5,13)(9,17)(12,18)(14,16)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1632);