Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #3993 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5 ⋊ #364 |
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)(7,12,15,14)(13,19,21,20);(2,3,4,5)(6,7,8,13,10,14,17,20,11,15,18,21,9,12,16,19)Polycyclic presentation:
2^6,5|a^2=c,b^2=de,c^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^2,g^c=g^444 conjugacy classes — view the full character table.
| maximal subgroup of | #10598744, #10598745, #10598750, … |
| maximal normal subgroup of | #10598744, #10598745, #10598750, … |
| maximal quotient of | #10598523, #10598525, #10598700, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 199);