Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C5×#99 ⋊ C2 |
| 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:
(1,2,4,5,3)(6,7)(8,10,12,13)(9,11);(2,3)(4,5)(7,10)(8,12)(11,13)Polycyclic presentation:
2^6,5|b^2=c,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^4,d^b=def,e^b=ef,d^c=df35 conjugacy classes — view the full character table.
| maximal subgroup of | #10599923, #10599926, #10599932, … |
| maximal normal subgroup of | #10599923, #10599926, #10599932, … |
| maximal quotient of | #10597939, #10597942, #10597944, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 32);