Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C5×C4⋊Q8 ⋊ C2 |
| Sylow | C5 ⋊ #486 |
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)(6,8,9,13)(7,11,10,12)(15,18)(16,21)(19,20);(6,7,9,10)(8,12,13,11);(2,3)(4,5)(7,10)(11,12)(14,15)(16,18)(17,20)(19,21)Polycyclic presentation:
2^6,5|b^2=e,c^2=e,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^4,c^b=ce,d^c=df50 conjugacy classes — view the full character table.
| maximal subgroup of | #10599225, #10599226, #10599239, … |
| maximal normal subgroup of | #10599225, #10599226, #10599239, … |
| maximal quotient of | #10600367, #10600373, #10600378, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 715);