Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×M16 ⋊ C4 |
| Sylow | C5 ⋊ #343 |
98 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)(6,7,8,11,9,10,12,13);(2,3,4,5)(7,10)(8,12)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,d^2=f,b^a=be,d^a=df,g^a=g^2,e^b=ef,g^c=g^432 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#100, #10603927, AGL(1,𝔽5)×#101, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#100, #10603927, AGL(1,𝔽5)×#101, … |
| maximal quotient of | #10598544, #10598545, #10598547, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 237);