Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| 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)(10,12,14,21,15,13,20,22)(11,16,18,24,19,17,23,25);(2,3,4,5)(7,9)(10,11,13,17,14,18,22,25,15,19,12,16,20,23,21,24)Polycyclic presentation:
2^6,5|a^2=c,b^2=de,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 | #10598615, #10598616, #10598617, … |
| maximal normal subgroup of | #10598615, #10598616, #10598617, … |
| maximal quotient of | #10598523, #10598525, #10598655, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 226);