Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #359 |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 37 points:
(1,2,3,5,4)(6,8,12,20)(7,13,16,30)(9,18,11,27)(10,23,25,37)(14,28,26,29)(15,31,32,34)(17,33,35,22)(19,21,36,24);(2,3,4,5)(6,7,9,14,12,16,11,26)(8,17,18,34,20,35,27,31)(10,22,21,32,25,33,24,15)(13,23,28,36,30,37,29,19)Polycyclic presentation:
2^6,5|a^2=c,b^2=f,c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^2,d^b=de,e^b=ef,g^c=g^429 conjugacy classes — view the full character table.
| maximal subgroup of | #10604128, #10604129, #10604136, … |
| maximal normal subgroup of | #10604128, #10604129, #10604136, … |
| maximal quotient of | #10598609, #10598613, #10598616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 247);