Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×Q16 ⋊ C4 |
| Sylow | C5 ⋊ #358 |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,5,4)(6,7,10,13)(8,15,17,21)(9,18,16,12)(11,19,20,14);(2,3,4,5)(7,11)(8,14)(9,16)(12,21)(13,20)(15,18)(17,19)Polycyclic presentation:
2^6,5|a^2=c,b^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^2,d^b=de,e^b=ef,g^c=g^429 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×SD32, #10604127, AGL(1,𝔽5)×Q32, … |
| maximal normal subgroup of | AGL(1,𝔽5)×SD32, #10604127, AGL(1,𝔽5)×Q32, … |
| maximal quotient of | #10598610, #10598612, #10598618, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 246);