Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×D8 ⋊ C4 |
| Sylow | C5 ⋊ #357 |
66 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)(7,11)(8,15)(9,16)(12,13)(14,20)(17,21)(18,19);(2,3,4,5)(6,7)(8,11)(9,18)(10,14)(12,15)(13,16)(17,20)(19,21)Polycyclic presentation:
2^6,5|a^2=c,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)×D16, #10604121, AGL(1,𝔽5)×SD32, … |
| maximal normal subgroup of | AGL(1,𝔽5)×D16, #10604121, AGL(1,𝔽5)×SD32, … |
| maximal quotient of | #10598609, #10598611, #10598617, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 242);