Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C71 ⋊ #1312 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4×C8 | C2×D71 |
| commutator | C2×C71 | C4×C16 |
| Fitting | C4×C16×C71 | C2 |
| socle | C22×C71 | C4×C8 |
| hypercenter | C4×C16 | D71 |
| hypocenter | C71 | #1312 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C4×C8 ◁ C4×C16 | |
92 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=c,b^2=d,c^2=e,d^2=f,f^2=g,b^a=be,h^a=h^702320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1312×D71, C2×#22586259, #31906440, … |
| maximal normal subgroup of | #1312×D71, C2×#22586259, #31906440, … |
| maximal quotient of | #31884069, #31884279, #31884784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2429);