Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×#103 ⋊ C2 |
| Sylow | C5 ⋊ #485 |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,4,5,3)(7,11)(10,13)(14,16,18,24)(15,20,19,22)(17,26,25,23)(21,28,27,29);(6,8,9,12)(7,10,11,13)(15,19)(16,23)(17,25)(20,28)(22,29)(24,26);(2,3)(4,5)(6,7)(8,10)(9,11)(12,13)(14,15)(16,22)(17,21)(18,19)(20,24)(23,28)(25,27)(26,29)Polycyclic presentation:
2^6,5|b^2=d,c^2=f,e^2=f,b^a=bf,c^a=cdf,g^a=g^4,c^b=ce,e^b=ef,e^c=ef47 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65104, #10610535, #10610538, … |
| maximal normal subgroup of | C2×#65104, #10610535, #10610538, … |
| maximal quotient of | #10599580, #10599605, #10599609, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 442);