Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C71 ⋊ #1398 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C4×Dic71 |
| commutator | C4×C71 | C4×C8 |
| Frattini | C2×C16 | C2×D71 |
| Fitting | M64×C71 | C2 |
| socle | C2×C71 | #346 |
| hypercenter | M64 | D71 |
| hypocenter | C71 | #1398 |
| LCS | G ▷ C4×C71 ▷ C71 | |
| UCS | C1 ◁ C8 ◁ M64 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bf,d^a=dg,c^b=cg,h^b=h^701444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1398×D71, C2×#22586475, #31917638, … |
| maximal normal subgroup of | #1398×D71, C2×#22586475, #31917638, … |
| maximal quotient of | #31884781, #31884786, #31885140, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2645);