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)(6,9,10,8)(7,11,12,13)(14,16,18,17)(15,20,19,21);(6,8,10,9)(7,11,12,13)(15,19)(20,21);(2,3,4,5)(6,7)(8,13)(9,11)(10,12)(14,15,17,20,18,19,16,21)Polycyclic presentation:
2^6,5|a^2=d,b^2=ef,c^2=e,d^2=f,b^a=be,c^a=cf,g^a=g^2,g^d=g^444 conjugacy classes — view the full character table.
| maximal subgroup of | #10598528, #10598533, #10598544, … |
| maximal normal subgroup of | #10598528, #10598533, #10598544, … |
| maximal quotient of | #10603790, #10603795, #10603834, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1022);