Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D5⋊#101 |
| Sylow | C5 ⋊ C2×#101 |
146 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3,5,4)(6,9,11,19)(7,13,15,17)(8,16,10,18)(12,20,14,21);(6,8,11,10)(7,12,15,14)(9,18,19,16)(13,21,17,20);(2,3,4,5)(6,7,10,14,11,15,8,12)(9,17,16,21,19,13,18,20)Polycyclic presentation:
2^6,5|a^2=d,b^2=f,c^2=f,d^2=f,c^a=ce,e^a=ef,g^a=g^2,c^b=cf,d^c=df,g^d=g^432 conjugacy classes — view the full character table.
| maximal subgroup of | #10598577, AGL(1,𝔽5)×#101, D5⋊#355, … |
| maximal normal subgroup of | #10598577, AGL(1,𝔽5)×#101, D5⋊#355, … |
| maximal quotient of | D5⋊#324, #10604291, #10604292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1127);