Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C5×Q16 ⋊ C2 |
| Sylow | C5 ⋊ #467 |
114 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)(10,12,14,20)(11,15,17,23)(13,21,22,19)(16,24,25,18);(10,11,13,16,14,17,22,25)(12,18,19,23,20,24,21,15);(2,3)(4,5)(6,7)(8,9)Polycyclic presentation:
2^6,5|b^2=e,c^2=f,e^2=f,c^a=cd,g^a=g^4,c^b=ce,e^c=ef50 conjugacy classes — view the full character table.
| maximal subgroup of | #10598813, #10598814, #10600007, … |
| maximal normal subgroup of | #10598813, #10598814, #10600007, … |
| maximal quotient of | #10601037, #10601041, #10601047, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 815);