Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #432 |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3,5,4)(7,11)(10,13)(15,18)(19,21);(6,8,9,12)(7,10,11,13)(15,18)(19,21);(2,3,4,5)(6,7)(8,10)(9,11)(12,13)(14,15,16,19,17,18,20,21)Polycyclic presentation:
2^6,5|a^2=d,b^2=e,d^2=f,b^a=bf,c^a=cef,g^a=g^2,g^d=g^444 conjugacy classes — view the full character table.
| maximal subgroup of | #10598505, #10598510, #10598557, … |
| maximal normal subgroup of | #10598505, #10598510, #10598557, … |
| maximal quotient of | #10604175, #10604181, #10604187, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1097);