Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×C4×C5 ⋊ C4 |
| Sylow | C5 ⋊ #381 |
218 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,3,5,4)(7,9)(10,12,13,16)(11,15,14,17);(11,14)(15,17);(2,3,4,5)(6,7)(8,9)(10,11)(12,15)(13,14)(16,17)Polycyclic presentation:
2^6,5|a^2=d,c^2=f,b^a=bf,c^a=ce,g^a=g^2,g^d=g^444 conjugacy classes — view the full character table.
| maximal subgroup of | #10598553, #10598555, #10598692, … |
| maximal normal subgroup of | #10598553, #10598555, #10598692, … |
| maximal quotient of | #10604158, #10604168, #10604184, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1102);