Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of D80 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #366 |
46 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,4,5,3)(10,11,16,22,13,17,20,23,14,18,24,25,19,21,12,15);(2,3)(4,5)(6,7,8,9)(11,15)(12,16)(13,19)(17,25)(18,23)(20,24)(21,22)Polycyclic presentation:
2^6,5|a^2=c,b^2=de,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^486 conjugacy classes — view the full character table.
| maximal subgroup of | #10598066, #10598067, #10598082, … |
| maximal normal subgroup of | #10598066, #10598067, #10598082, … |
| maximal quotient of | #10597991, #10598082, #10598083, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 62);