Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#100 ⋊ C2 |
| Sylow | C5 ⋊ #455 |
152 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)(6,8,9,16,10,15,18,21)(7,11,12,14,13,19,17,20);(8,15)(9,18)(12,17)(14,20);(2,3)(4,5)(6,7)(8,14)(9,17)(10,13)(11,16)(12,18)(15,20)(19,21)Polycyclic presentation:
2^6,5|c^2=d,d^2=f,c^a=cd,d^a=df,e^a=ef,g^a=g^4,c^b=ce,d^b=df,e^c=ef38 conjugacy classes — view the full character table.
| maximal subgroup of | #10598572, #10599924, #10599925, … |
| maximal normal subgroup of | #10598572, #10599924, #10599925, … |
| maximal quotient of | #10598901, #10598902, #10598903, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 373);