Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #408 |
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:
(1,2,3,5,4)(7,9)(10,13,15,14)(11,17,19,18)(12,20,21,22)(16,23,24,25);(10,12,15,21)(11,16,19,24)(13,22,14,20)(17,25,18,23);(2,3,4,5)(6,7)(8,9)(10,11,14,18,15,19,13,17)(12,16,20,23,21,24,22,25)Polycyclic presentation:
2^6,5|a^2=d,b^2=f,c^2=f,d^2=f,c^a=ce,g^a=g^2,c^b=cf,g^d=g^438 conjugacy classes — view the full character table.
| maximal subgroup of | #10598578, #10603934, #10603987, … |
| maximal normal subgroup of | #10598578, #10603934, #10603987, … |
| maximal quotient of | #10604296, #10604299, #10604300, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1125);