Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q64×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2262 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D16×D71 |
| commutator | C16×C71 | C23 |
| Frattini | C16 | C22×D71 |
| Fitting | Q64×C71 | C2 |
| socle | C2×C71 | C2×D16 |
| hypercenter | Q64 | D71 |
| hypocenter | C71 | #2262 |
| LCS | G ▷ C16×C71 ▷ C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q64 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|c^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,d^a=de,e^a=ef,f^a=fg,h^a=h^70,d^b=de,e^b=ef,f^b=fg,h^b=h^70,h^c=h^70703 conjugacy classes — view the full character table.
| maximal subgroup of | #31918505, #31918507, #31918511, … |
| maximal normal subgroup of | #31918505, #31918507, #31918511, … |
| maximal quotient of | #31917885, #31917952, #31918025, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6820);