Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C5×#97 ⋊ C2 |
| 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)(10,12,13,20,14,19,22,25)(11,16,17,18,15,23,21,24);(6,7,8,9)(11,15)(12,19)(17,21)(20,25);(2,3)(4,5)(7,9)(10,11)(12,18)(13,21)(14,15)(16,20)(17,22)(19,24)(23,25)Polycyclic presentation:
2^6,5|b^2=ef,c^2=d,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^4,c^b=cf56 conjugacy classes — view the full character table.
| maximal subgroup of | #10598541, #10599145, #10599150, … |
| maximal normal subgroup of | #10598541, #10599145, #10599150, … |
| maximal quotient of | #10598883, #10598886, #10598888, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 342);