Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4×C5×Q8 ⋊ D3 |
| derived | C5×SL(2,𝔽3) ⋊ C2×C4 |
| Sylow | C5 ⋊ #5394 |
154 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^3,3,5,2^3|b^2=c,f^2=h,g^2=h,b^a=bh,d^a=d^2,e^a=e^4,f^a=gh,g^a=fh,f^d=g,g^d=fgh,g^f=gh82 conjugacy classes — view the full character table.
| maximal subgroup of | #14512609, #14512625, #14512635, … |
| maximal normal subgroup of | #14512609, #14512625, #14512635, … |
| maximal quotient of | #14511933, #14511934, #14511976, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6308);