Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64707 |
| 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)(6,8,9,14,12,17,11,7)(10,19,18,21,20,13,15,16);(2,3)(4,5)(6,7,10,13,11,8,15,16,12,14,20,19,9,17,18,21)Polycyclic presentation:
2^6,5|a^2=d,b^2=c,c^2=f,d^2=e,e^2=f,b^a=bde,c^a=cf,g^a=g^4,d^b=de,e^b=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | #10600047, #10600050, #10600057, … |
| maximal normal subgroup of | #10600047, #10600050, #10600057, … |
| maximal quotient of | #10597955, #10598221, C2×#64714, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 52);