Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,4,5,3)(7,9)(10,11,12,15,13,16,18,21,14,17,19,22,20,23,24,25);(2,3)(4,5)(6,7,8,9)Polycyclic presentation:
2^6,5|a^2=d,b^2=c,c^2=e,e^2=f,b^a=bd,g^a=g^4104 conjugacy classes — view the full character table.
| maximal subgroup of | C16×Dic10, #10599841, #10599845, … |
| maximal normal subgroup of | C16×Dic10, #10599841, #10599845, … |
| maximal quotient of | #10598045, #10598046, #10598081, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 59);