Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #336 |
118 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)(11,13)(14,15,16,18,17,19,20,21);(2,3)(4,5)(6,7,8,9)(10,11)(12,13)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,d^2=f,b^a=be,g^a=g^4104 conjugacy classes — view the full character table.
| maximal subgroup of | #10599389, #10599390, #10599391, … |
| maximal normal subgroup of | #10599389, #10599390, #10599391, … |
| maximal quotient of | #10598144, #10598146, #10598147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 108);