Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C5×M16 ⋊ C2 |
| Sylow | C5 ⋊ #408 |
158 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,4,5,3)(7,9)(10,12,13,19,14,18,20,24)(11,16,17,23,15,21,22,25);(11,15)(12,18)(17,22)(19,24);(2,3)(4,5)(6,7)(8,9)(10,11)(12,16)(13,17)(14,15)(18,21)(19,23)(20,22)(24,25)Polycyclic presentation:
2^6,5|c^2=d,d^2=f,b^a=bf,c^a=ce,g^a=g^4,c^b=cf68 conjugacy classes — view the full character table.
| maximal subgroup of | #10598022, #10598781, #10598790, … |
| maximal normal subgroup of | #10598022, #10598781, #10598790, … |
| maximal quotient of | #10600623, #10600630, #10600631, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 756);