Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #427 |
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)(6,7,8,9)(11,16)(12,19)(13,21)(15,22)(17,18)(23,24);(10,12)(11,15)(13,20)(14,19)(16,24)(17,22)(18,23)(21,25);(2,3)(4,5)(10,11,13,17,14,18,21,16)(12,15,20,22,19,23,25,24)Polycyclic presentation:
2^6,5|a^2=e,c^2=d,e^2=f,c^a=ce,g^a=g^4,c^b=cf,e^c=ef68 conjugacy classes — view the full character table.
| maximal subgroup of | #10599492, #10599503, #10599531, … |
| maximal normal subgroup of | #10599492, #10599503, #10599531, … |
| maximal quotient of | #10600261, C4×#3940, C4×#3939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 625);