Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C5×#97 ⋊ C2 |
| Sylow | C5 ⋊ C4×M16 |
142 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)(10,11,12,15,13,14,16,17);(6,7,8,9)(11,14)(15,17);(2,3)(4,5)(11,14)(15,17)Polycyclic presentation:
2^6,5|b^2=e,c^2=d,d^2=f,c^a=cf,g^a=g^4,c^b=cf80 conjugacy classes — view the full character table.
| maximal subgroup of | #10598543, #10598548, #10599134, … |
| maximal normal subgroup of | #10598543, #10598548, #10599134, … |
| maximal quotient of | #10598860, #10598863, #10598865, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 334);