Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C71 ⋊ #2110 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C4×Dic71 |
| commutator | C4×C71 | C2×C42 |
| Frattini | C2×C8 | C22×D71 |
| Fitting | #405×C71 | C2 |
| socle | C2×C71 | C2×#97 |
| hypercenter | #405 | D71 |
| hypocenter | C71 | #2110 |
| LCS | G ▷ C4×C71 ▷ C71 | |
| UCS | C1 ◁ C8 ◁ #405 | |
160 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bf,e^a=eg,h^a=h^70,c^b=cg,d^b=dg1444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31908634, #31908635, #31908638, … |
| maximal normal subgroup of | #31908634, #31908635, #31908638, … |
| maximal quotient of | #31906457, #31906461, #31906494, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6115);