Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C5 ⋊ #487 |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(7,11)(10,12)(14,15,17,19)(16,21,20,18);(6,8,9,13)(7,10,11,12)(15,18)(16,20)(19,21);(2,3)(4,5)(6,7,9,11)(8,12,13,10)Polycyclic presentation:
2^6,5|a^2=e,b^2=e,c^2=f,d^2=f,b^a=be,c^a=ce,g^a=g^4,c^b=cd,d^b=df,d^c=df50 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65081, #10610516, #10610536, … |
| maximal normal subgroup of | C2×#65081, #10610516, #10610536, … |
| maximal quotient of | #10599596, #10599604, #10599636, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 419);