Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×C22⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ #352 |
68 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)(6,8)(7,11,14,21)(9,16)(10,18)(12,15,13,20)(17,19);(2,3,4,5)(6,7,9,12,10,14,19,13)(8,15,16,11,18,20,17,21)Polycyclic presentation:
2^6,5|a^2=c,b^2=e,c^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^2,c^b=ce,d^b=df,d^c=df,g^c=g^423 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#64865, #10604213, #10604381, … |
| maximal normal subgroup of | C2×#64865, #10604213, #10604381, … |
| maximal quotient of | #10598496, #10598498, #10598500, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 203);