Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #346 |
54 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)(10,12,21,23,14,22,15,13)(11,16,24,17,18,20,19,25);(2,3,4,5)(10,11,13,17,15,19,22,16,14,18,23,25,21,24,12,20)Polycyclic presentation:
2^6,5|a^2=c,b^2=de,c^2=e,e^2=f,b^a=bf,g^a=g^2,g^c=g^456 conjugacy classes — view the full character table.
| maximal subgroup of | #10598607, #10598608, #10598638, … |
| maximal normal subgroup of | #10598607, #10598608, #10598638, … |
| maximal quotient of | #10598512, #10598513, #10598656, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 224);