Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C5×C8 ⋊ C2 |
| Sylow | C5 ⋊ #431 |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(6,7,8,10,9,11,12,13)(15,19)(18,21);(14,16,17,20)(15,18,19,21);(2,3)(4,5)(14,15)(16,18)(17,19)(20,21)Polycyclic presentation:
2^6,5|b^2=e,c^2=d,d^2=f,c^a=ce,g^a=g^4104 conjugacy classes — view the full character table.
| maximal subgroup of | #10598526, #10598527, #10598529, … |
| maximal normal subgroup of | #10598526, #10598527, #10598529, … |
| maximal quotient of | #10599398, #10599400, #10599448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 312);