Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C5×C8 ⋊ C4 |
| Sylow | C5 ⋊ #344 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,5,4)(6,8,9,16,10,15,17,21)(7,11,12,18,13,14,19,20);(2,3,4,5)(6,7)(8,14,15,11)(9,12)(10,13)(16,20,21,18)(17,19)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,d^2=f,b^a=be,e^a=ef,g^a=g^2,c^b=cf,g^c=g^438 conjugacy classes — view the full character table.
| maximal subgroup of | #10603852, #10603853, #10603886, … |
| maximal normal subgroup of | #10603852, #10603853, #10603886, … |
| maximal quotient of | #10598527, #10598528, #10598532, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 232);