Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #475 |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(6,9,10,8)(7,11,12,13)(14,15,17,19)(16,21,20,18);(6,8,10,9)(7,11,12,13)(15,18)(16,20)(19,21);(2,3)(4,5)(6,7,10,12)(8,13,9,11)Polycyclic presentation:
2^6,5|a^2=e,b^2=e,c^2=ef,d^2=f,b^a=be,g^a=g^4,c^b=cd,d^b=df,d^c=df47 conjugacy classes — view the full character table.
| maximal subgroup of | #10610855, #10610857, #10610861, … |
| maximal normal subgroup of | #10610855, #10610857, #10610861, … |
| maximal quotient of | #10599581, #10599593, #10599603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 481);