Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C43×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2293 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D71 |
| commutator | C22×C71 | C23×C4 |
| Frattini | C23 | C23×D71 |
| Fitting | C43×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C43 | D71 |
| hypocenter | C71 | #2293 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C43 | |
652 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|a^2=g,b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^702296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31885389, #31885392, #31885444, … |
| maximal normal subgroup of | #31885389, #31885392, #31885444, … |
| maximal quotient of | #31918563, #31918594, C4×#17985890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6974);