Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64757 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #333 |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(7,10)(8,12)(14,15,17,19)(16,21,20,18);(2,3)(4,5)(6,7,8,11,9,10,12,13)(15,18)(16,20)(19,21)Polycyclic presentation:
2^6,5|a^2=c,b^2=f,c^2=e,d^2=f,b^a=bd,d^a=def,g^a=g^4,c^b=ce,d^b=df47 conjugacy classes — view the full character table.
| maximal subgroup of | #10598041, #10598264, D5×#333, … |
| maximal normal subgroup of | #10598041, #10598264, D5×#333, … |
| maximal quotient of | #10598125, #10598133, #10598291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 104);