Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C5×M16 ⋊ C2 |
| Sylow | C5 ⋊ #469 |
130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,4,5,3)(7,9)(11,16)(14,17);(10,11,15,17,13,16,12,14);(2,3)(4,5)(6,7)(8,9)(11,14)(12,15)(16,17)Polycyclic presentation:
2^6,5|b^2=ef,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^4,c^b=cf56 conjugacy classes — view the full character table.
| maximal subgroup of | #10597972, #10597974, #10598025, … |
| maximal normal subgroup of | #10597972, #10597974, #10598025, … |
| maximal quotient of | #10600611, #10600613, #10600618, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 762);