Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #431 |
118 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)(6,7,8,10,9,11,12,13)(16,20)(18,21);(14,16)(15,18)(17,20)(19,21);(2,3)(4,5)(14,15,17,19)(16,18,20,21)Polycyclic presentation:
2^6,5|a^2=e,c^2=d,d^2=f,g^a=g^4,c^b=ce80 conjugacy classes — view the full character table.
| maximal subgroup of | #10598556, #10598557, #10598562, … |
| maximal normal subgroup of | #10598556, #10598557, #10598562, … |
| maximal quotient of | #10599389, #10599395, #10599398, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 345);