Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #497 |
124 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,4,5,3)(7,9)(11,16)(12,19)(13,21)(15,22)(17,18)(23,24);(6,7,8,9)(10,12)(11,15)(13,20)(14,19)(16,24)(17,22)(18,23)(21,25);(2,3)(4,5)(7,9)(10,11,14,18)(12,15,19,23)(13,16,21,17)(20,24,25,22)Polycyclic presentation:
2^6,5|a^2=f,b^2=e,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^4,c^b=cef,d^c=df44 conjugacy classes — view the full character table.
| maximal subgroup of | #10598036, #10598040, #10599146, … |
| maximal normal subgroup of | #10598036, #10598040, #10599146, … |
| maximal quotient of | #10600343, #10600345, #10600354, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 687);