Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×C4⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #476 |
108 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)(7,11)(8,12)(14,15,16,18,17,19,20,21);(6,8,9,12)(7,10,11,13);(2,3)(4,5)(6,7)(8,10)(9,11)(12,13)(15,18)(16,20)(19,21)Polycyclic presentation:
2^6,5|b^2=e,c^2=de,d^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=ce59 conjugacy classes — view the full character table.
| maximal subgroup of | #10598974, #10598988, #10598996, … |
| maximal normal subgroup of | #10598974, #10598988, #10598996, … |
| maximal quotient of | #10599416, #10599426, #10599436, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 469);