Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #416 |
158 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)(11,16)(13,21)(15,22)(17,18)(19,25)(23,24);(10,12,14,20)(11,15,18,24)(13,19,21,25)(16,22,17,23);(2,3)(4,5)(6,7,8,9)(10,11)(12,15)(13,16)(14,18)(17,21)(19,22)(20,24)(23,25)Polycyclic presentation:
2^6,5|a^2=e,b^2=f,d^2=f,c^a=cd,d^a=df,g^a=g^4,d^c=df68 conjugacy classes — view the full character table.
| maximal subgroup of | #10600789, #10600790, #10600791, … |
| maximal normal subgroup of | #10600789, #10600790, #10600791, … |
| maximal quotient of | #10602368, #10602373, #10602398, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 860);