Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C24×C5 ⋊ C4 |
| Sylow | C5 ⋊ AΣL(1,𝔽16) |
94 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)(11,12);(2,3,4,5)(6,7)(8,12,13,10)(9,11)Polycyclic presentation:
2^6,5|a^2=c,b^a=bd,d^a=de,e^a=ef,g^a=g^2,c^b=ce,d^c=df,g^c=g^429 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊AΣL(1,𝔽16), #10604458, #10604459, … |
| maximal normal subgroup of | D5⋊AΣL(1,𝔽16), #10604458, #10604459, … |
| maximal quotient of | #10598820, #10598822, #10598825, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 272);