Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×#41×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3038 |
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^70,f^c=fg1432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31893343, #31893345, #31893350, … |
| maximal normal subgroup of | #31893343, #31893345, #31893350, … |
| maximal quotient of | #31981338, #31981347, #31981354, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 13990);