Finite Group DatabasebetaFinite Group Databasebeta| order | 160 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | Aut(G) = C4×#87524 (order 1536) · Inn(G) = C23 · Out(G) = C2×C4×S4 |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#120 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C23 |
| commutator, Frattini, cosocle | C22 | C23×C5 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ G | |
130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 3 generators on 13 points:
(1,2)(3,4)(5,6)(7,8)(9,10,11,12,13);(2,4);(6,8)70 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(160, 181);