Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64671 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #332 |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(7,10)(8,13)(11,12)(14,15,16,20,18,21,17,19);(2,3)(4,5)(6,7,9,12)(8,10,13,11)(15,19)(16,17)(20,21)Polycyclic presentation:
2^6,5|a^2=e,b^2=c,c^2=ef,d^2=f,b^a=bd,c^a=cef,d^a=df,g^a=g^4,d^b=de59 conjugacy classes — view the full character table.
| maximal subgroup of | #10598978, #10598986, #10598993, … |
| maximal normal subgroup of | #10598978, #10598986, #10598993, … |
| maximal quotient of | #10597968, #10598054, #10598055, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 44);