Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C42×C5 ⋊ C4 |
| Sylow | C5 ⋊ #353 |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 2 generators on 13 points:
(1,2,3,5,4)(7,10,12,11);(2,3,4,5)(6,7)(8,11,13,10)(9,12)Polycyclic presentation:
2^6,5|a^2=c,b^2=e,d^2=f,b^a=bd,d^a=def,e^a=ef,g^a=g^2,c^b=ce,d^c=df,g^c=g^429 conjugacy classes — view the full character table.
| maximal subgroup of | #10598516, #10598517, #10598539, … |
| maximal normal subgroup of | #10598516, #10598517, #10598539, … |
| maximal quotient of | #10598495, #10598498, #10598516, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 191);