Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#101 ⋊ C2 |
| Sylow | C5 ⋊ #473 |
100 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,4,5,3)(6,9,11,22)(7,13,15,28)(8,16,18,20)(10,23,24,21)(12,25,27,36)(14,29,30,19)(17,33,34,32)(26,31,37,35);(6,8,10,17,11,18,24,34)(7,12,14,26,15,27,30,37)(9,20,21,33,22,16,23,32)(13,25,19,35,28,36,29,31);(2,3)(4,5)(6,7)(8,12)(9,19)(10,14)(11,15)(13,23)(16,31)(17,26)(18,27)(20,35)(21,28)(22,29)(24,30)(25,32)(33,36)(34,37)Polycyclic presentation:
2^6,5|b^2=d,c^2=f,d^2=f,c^a=cde,e^a=ef,g^a=g^4,c^b=cef,e^b=ef,d^c=df38 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65044, #10610443, #10610450, … |
| maximal normal subgroup of | C2×#65044, #10610443, #10610450, … |
| maximal quotient of | #10599234, #10599236, #10599237, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 382);