Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #324 |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(6,7,8,10,9,11,12,13)(14,16)(15,18,19,20)(17,21);(2,3)(4,5)(14,15,17,19)(16,20,21,18)Polycyclic presentation:
2^6,5|a^2=f,b^2=c,c^2=e,b^a=bd,c^a=cf,g^a=g^4,d^b=df62 conjugacy classes — view the full character table.
| maximal subgroup of | #10598893, #10598895, #10598898, … |
| maximal normal subgroup of | #10598893, #10598895, #10598898, … |
| maximal quotient of | #10597937, #10597938, #10597943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 27);