Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #376×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2397 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D71 |
| commutator, socle | C23×C71 | C24 |
| Frattini | C23 | C23×D71 |
| Fitting | #376×C71 | C2 |
| hypercenter | #376 | D71 |
| hypocenter | C71 | #2397 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
840 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=e,d^2=ef,b^a=be,c^a=cf,c^b=cg,h^b=h^70,h^c=h^701444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31892530, #31898292, #31898295, … |
| maximal normal subgroup of | #31892530, #31898292, #31898295, … |
| maximal quotient of | #31919188, #31919234, C4×#17985909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 7791);