Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64733 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5 ⋊ #365 |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(6,7,8,11,9,13,14,18,10,12,15,17,16,19,21,20);(2,3)(4,5)(7,11,12,17)(8,14)(9,16)(13,20,19,18)(15,21)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,d^2=e,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^4,c^b=cf56 conjugacy classes — view the full character table.
| maximal subgroup of | #10599883, #10599884, #10599909, … |
| maximal normal subgroup of | #10599883, #10599884, #10599909, … |
| maximal quotient of | #10598004, #10598307, C2×#64733, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 71);