Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C71 ⋊ #1313 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic71 |
| commutator | C4×C71 | C4×C8 |
| Frattini | C4×C8 | C2×D71 |
| Fitting | #322×C71 | C2 |
| socle | C22×C71 | #97 |
| hypercenter | #322 | D71 |
| hypocenter | C71 | #1313 |
| LCS | G ▷ C4×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ #322 | |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=be,d^a=dg,h^a=h^70,c^b=cg1444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1313×D71, C2×#22586261, #31906451, … |
| maximal normal subgroup of | #1313×D71, C2×#22586261, #31906451, … |
| maximal quotient of | #31884069, #31884282, #31884788, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2431);