Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#674 |
| Sylow | C5 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3,5,4)(6,7,8,9);(2,3,4,5)(7,9)(10,11,12,15,13,16,18,21,14,17,19,22,20,23,24,25)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,c^2=e,e^2=f,b^a=bd,g^a=g^2,g^c=g^456 conjugacy classes — view the full character table.
| maximal subgroup of | #10598522, #10598523, #10598524, … |
| maximal normal subgroup of | #10598522, #10598523, #10598524, … |
| maximal quotient of | #10598522, #10598524, C4⋊#3928, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 196);