Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C4⋊C8×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3245 |
436 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^70,c^b=ce,f^c=fg,h^c=h^701432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31898384, #31898385, #31898396, … |
| maximal normal subgroup of | #31898384, #31898385, #31898396, … |
| maximal quotient of | #32007333, #32007833, #32009492, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 15820);