Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,4,5,3)(6,8,9,7)(12,18)(13,21)(15,22)(16,25)(19,20)(23,24);(6,7,9,8)(10,12)(11,15)(13,18)(14,20)(16,22)(17,24)(19,21)(23,25);(2,3)(4,5)(6,7,9,8)(10,11,14,17)(12,15,20,24)(13,16,21,25)(18,22,19,23)Polycyclic presentation:
2^6,5|a^2=e,b^2=ef,c^2=ef,d^2=f,g^a=g^4,c^b=cd,d^b=df,d^c=df56 conjugacy classes — view the full character table.
| maximal subgroup of | #10598608, #10598610, #10599968, … |
| maximal normal subgroup of | #10598608, #10598610, #10599968, … |
| maximal quotient of | #10599350, #10599353, #10599357, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 500);