Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ Q8⋊C8 |
70 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)(6,7,8,10,9,11,12,13)(15,18)(16,21)(19,20);(2,3)(4,5)(14,15,17,20)(16,18,21,19)Polycyclic presentation:
2^6,5|a^2=f,b^2=c,c^2=e,d^2=f,b^a=bd,d^a=df,g^a=g^4,d^b=df68 conjugacy classes — view the full character table.
| maximal subgroup of | #10598958, #10598959, #10598962, … |
| maximal normal subgroup of | #10598958, #10598959, #10598962, … |
| maximal quotient of | #10597968, #10597971, #10598049, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 42);