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:
(1,2,4,5,3)(8,12)(10,13)(14,15,16,19,17,18,20,21);(6,8)(7,10)(9,12)(11,13);(2,3)(4,5)(6,7,9,11)(8,10,12,13)(15,18)(19,21)Polycyclic presentation:
2^6,5|a^2=e,c^2=d,d^2=f,c^a=cf,g^a=g^4,c^b=ce68 conjugacy classes — view the full character table.
| maximal subgroup of | #10598558, #10598564, #10598565, … |
| maximal normal subgroup of | #10598558, #10598564, #10598565, … |
| maximal quotient of | #10599390, #10599396, #10599398, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 346);