Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of D80 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #358 |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,4,5,3)(6,8,9,7)(10,11,16,25,14,18,12,15,13,17,19,24,20,22,21,23);(2,3)(4,5)(6,7,9,8)(11,15)(12,19)(14,20)(16,21)(17,23)(18,25)(22,24)Polycyclic presentation:
2^6,5|a^2=df,b^2=cde,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^486 conjugacy classes — view the full character table.
| maximal subgroup of | #10599852, C4×#3932, C4×Dic40, … |
| maximal normal subgroup of | #10599852, C4×#3932, C4×Dic40, … |
| maximal quotient of | #10597996, #10598019, #10598052, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 61);