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)(7,13)(9,18)(10,23)(11,27)(12,20)(14,28)(15,31)(16,30)(17,22)(19,24)(21,35)(25,37)(26,29)(32,33)(34,36);(2,3,4,5)(6,7,9,14,12,16,11,26)(8,17,18,33,20,34,27,31)(10,22,21,32,25,36,24,15)(13,23,28,35,30,37,29,19)Polycyclic presentation:
2^6,5|a^2=c,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 | #10604122, #10604123, #10604128, … |
| maximal normal subgroup of | #10604122, #10604123, #10604128, … |
| maximal quotient of | #10598610, #10598614, #10598615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 243);