Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×M32 ⋊ C2 |
| Sylow | C5 ⋊ #349 |
58 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)(6,7,8,12,9,13,15,19,10,11,14,17,16,18,20,21);(2,3)(4,5)(7,11)(8,14)(13,18)(15,20)Polycyclic presentation:
2^6,5|b^2=c,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^4,d^b=df62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599881, #10599882, D5×#349, … |
| maximal normal subgroup of | #10599881, #10599882, D5×#349, … |
| maximal quotient of | #10598006, #10598009, #10598013, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 72);