Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#101 ⋊ C2 |
| Sylow | C5 ⋊ #413 |
150 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(6,8,9,15,10,16,18,21)(7,12,13,19,11,14,17,20);(6,7,10,11)(8,14,16,12)(9,17,18,13)(15,19,21,20);(2,3)(4,5)(7,11)(12,14)(13,17)(19,20)Polycyclic presentation:
2^6,5|b^2=f,c^2=d,d^2=f,b^a=bf,g^a=g^4,c^b=ce,d^b=df,e^c=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | #10598578, #10599958, #10599959, … |
| maximal normal subgroup of | #10598578, #10599958, #10599959, … |
| maximal quotient of | #10598917, #10598919, #10598922, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 378);