Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64868 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×C4⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ #327 |
90 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)(6,8,9,13)(7,10,11,12)(15,18)(16,21)(19,20);(2,3,4,5)(6,7)(8,12,13,10)(9,11)(14,15)(16,18)(17,20)(19,21)Polycyclic presentation:
2^6,5|a^2=c,b^2=e,d^2=f,b^a=bd,d^a=def,g^a=g^2,c^b=ce,d^b=df,g^c=g^429 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#64868, #10604258, #10604260, … |
| maximal normal subgroup of | C2×#64868, #10604258, #10604260, … |
| maximal quotient of | #10598495, #10598496, #10598499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 206);