Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64849 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×C16 ⋊ C4 |
| Sylow | C5 ⋊ #367 |
46 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)(6,7,12,18,17,21,8,11,10,14,15,20,9,13,16,19);(2,3,4,5)(7,11)(8,15)(9,17)(12,16)(13,20)(14,19)(18,21)Polycyclic presentation:
2^6,5|a^2=c,b^2=de,d^2=e,e^2=f,b^a=bd,d^a=def,e^a=ef,g^a=g^2,g^c=g^438 conjugacy classes — view the full character table.
| maximal subgroup of | #10598491, #10598492, #10598679, … |
| maximal normal subgroup of | #10598491, #10598492, #10598679, … |
| maximal quotient of | #10598491, #10598492, #10598646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 188);