Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C5×D4 ⋊ 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)(8,13)(11,12);(2,3,4,5)(6,7)(8,11,13,10)(9,12)Polycyclic presentation:
2^6,5|a^2=c,d^2=f,b^a=bd,d^a=def,e^a=ef,g^a=g^2,c^b=ce,d^b=df,d^c=df,g^c=g^423 conjugacy classes — view the full character table.
| maximal subgroup of | #10598571, #10598833, #10604545, … |
| maximal normal subgroup of | #10598571, #10598833, #10604545, … |
| maximal quotient of | #10598711, #10598717, #10598723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 260);