Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C5 ⋊ #489 |
100 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)(10,12)(14,15)(16,21)(17,18)(19,20);(6,8,9,13)(7,10,11,12)(15,19)(16,20)(18,21);(2,3)(4,5)(6,7,9,11)(8,12,13,10)(15,18)(19,21)Polycyclic presentation:
2^6,5|a^2=e,b^2=e,d^2=f,b^a=be,c^a=cef,g^a=g^4,c^b=cd,d^b=df,d^c=df44 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65054, #10610468, #10610492, … |
| maximal normal subgroup of | C2×#65054, #10610468, #10610492, … |
| maximal quotient of | #10599599, #10599637, #10599639, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 392);