Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C71 ⋊ #1311 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4×C8 | C2×D71 |
| commutator | C2×C71 | C82 |
| Fitting | C4×C16×C71 | C2 |
| socle | C22×C71 | C4×C8 |
| hypercenter | C4×C16 | D71 |
| hypocenter | C71 | #1311 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C4×C8 ◁ C4×C16 | |
96 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=bg,h^b=h^702320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31884781, #31884786, #31885119, … |
| maximal normal subgroup of | #31884781, #31884786, #31885119, … |
| maximal quotient of | #31884066, #31884067, #31884279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2426);