Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5 ⋊ #365 |
| Sylow | C5 ⋊ #4494 |
| Sylow | C3 ⋊ ΓL(1,𝔽81) |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|a^2=c,b^2=df,c^2=f,d^2=e,e^2=f,b^a=bd,d^a=de,e^a=ef,h^a=h^2,c^b=cf,g^b=g^2,h^c=h^454 conjugacy classes — view the full character table.
| maximal subgroup of | D3×ΓL(1,𝔽81), #14314494, C2×#11746475, … |
| maximal normal subgroup of | D3×ΓL(1,𝔽81), #14314494, C2×#11746475, … |
| maximal quotient of | #14278601, #14278602, #14278899, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 670);