Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C5 ⋊ #491 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,4,5,3)(7,11)(10,12)(14,16,24,28,18,23,17,25)(15,20,26,29,19,27,21,22);(6,8,9,13)(7,10,11,12)(15,19)(16,23)(21,26)(25,28);(2,3)(4,5)(6,7,9,11)(8,12,13,10)(14,15,18,19)(16,22,23,29)(17,26,24,21)(20,28,27,25)Polycyclic presentation:
2^6,5|a^2=e,b^2=ef,c^2=de,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^4,c^b=cf56 conjugacy classes — view the full character table.
| maximal subgroup of | #10598012, #10598542, #10599151, … |
| maximal normal subgroup of | #10598012, #10598542, #10599151, … |
| maximal quotient of | #10599424, #10599431, #10599435, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 330);