Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #381 |
218 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)(6,7,8,9)(11,13)(16,20)(18,21);(14,16)(15,18)(17,20)(19,21);(2,3)(4,5)(10,11)(12,13)(14,15,17,19)(16,18,20,21)Polycyclic presentation:
2^6,5|a^2=f,c^2=d,c^a=ce,g^a=g^4,c^b=cf68 conjugacy classes — view the full character table.
| maximal subgroup of | #10597936, #10598703, #10598708, … |
| maximal normal subgroup of | #10597936, #10598703, #10598708, … |
| maximal quotient of | #10600195, #10600215, #10600216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 570);