Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C5×C8 ⋊ C2 |
| Sylow | C5 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(6,7,8,10,9,11,12,13)(15,19,21,20);(2,3)(4,5)(14,15)(16,19)(17,20)(18,21)Polycyclic presentation:
2^6,5|b^2=cd,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^492 conjugacy classes — view the full character table.
| maximal subgroup of | C8×D40, #10598845, C8×#677, … |
| maximal normal subgroup of | C8×D40, #10598845, C8×#677, … |
| maximal quotient of | #10597932, #10597934, #10597968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 17);