Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #419 |
150 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)(6,8,9,7)(10,13,14,21,15,22,12,19)(11,17,16,20,18,25,23,24);(10,12,15,14)(11,16,18,23)(13,21,22,19)(17,24,25,20);(2,3)(4,5)(6,7,9,8)(10,11)(12,16)(13,20)(14,23)(15,18)(17,21)(19,25)(22,24)Polycyclic presentation:
2^6,5|a^2=e,b^2=f,c^2=de,d^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=cf62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599505, #10599518, #10599552, … |
| maximal normal subgroup of | #10599505, #10599518, #10599552, … |
| maximal quotient of | #10600606, #10600615, #10600621, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 747);