Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #356 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(6,8,11,9)(7,12,15,20)(10,18,19,17)(13,21,16,14);(2,3)(4,5)(6,7,9,13,11,15,8,16)(10,14,17,20,19,21,18,12)Polycyclic presentation:
2^6,5|a^2=c,b^2=f,c^2=f,d^2=f,b^a=bd,d^a=def,e^a=ef,g^a=g^4,c^b=ce,d^b=df,d^c=df41 conjugacy classes — view the full character table.
| maximal subgroup of | #10597954, #10598042, #10598043, … |
| maximal normal subgroup of | #10597954, #10598042, #10598043, … |
| maximal quotient of | #10598126, #10598134, #10598135, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 106);