Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #323 |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,5,4)(14,16)(15,18)(17,21)(19,20);(2,3,4,5)(6,7,8,10,9,11,12,13)(14,15)(16,20,21,18)(17,19)Polycyclic presentation:
2^6,5|a^2=c,c^2=e,b^a=bd,d^a=df,g^a=g^2,c^b=cf,g^c=g^438 conjugacy classes — view the full character table.
| maximal subgroup of | #10598702, #10598703, #10598704, … |
| maximal normal subgroup of | #10598702, #10598703, #10598704, … |
| maximal quotient of | #10598817, #10598818, #10598819, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 271);