Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #355 |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,5,4)(7,11,14,13)(8,15)(12,19,20,21)(16,17);(2,3,4,5)(6,7,8,12,10,14,15,20)(9,11,17,19,18,13,16,21)Polycyclic presentation:
2^6,5|a^2=c,b^2=e,c^2=f,d^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^2,c^b=cef,d^c=df,g^c=g^429 conjugacy classes — view the full character table.
| maximal subgroup of | #10598518, #10598519, #10598540, … |
| maximal normal subgroup of | #10598518, #10598519, #10598540, … |
| maximal quotient of | #10598499, #10598501, #10598686, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 194);