Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64845 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5 ⋊ #347 |
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)(7,11,13,14)(8,15)(12,20,21,19)(16,18);(2,3,4,5)(6,7,8,12,9,14,16,20,10,13,15,21,17,11,18,19)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,c^2=e,e^2=f,b^a=be,d^a=df,g^a=g^2,c^b=cf,g^c=g^438 conjugacy classes — view the full character table.
| maximal subgroup of | #10598734, #10598735, #10598736, … |
| maximal normal subgroup of | #10598734, #10598735, #10598736, … |
| maximal quotient of | #10598515, #10598699, C2×#64860, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 198);