Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Fitting | #322×C71 ⋊ C2 |
| Sylow | C71 ⋊ #1453 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D71 |
| commutator, socle | C22×C71 | C2×C42 |
| Fitting | #322×C71 | C2 |
| hypercenter | #322 | D71 |
| hypocenter | C71 | #1453 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C42 ◁ #322 | |
190 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=d,b^2=e,d^2=f,e^2=g,c^a=cg,h^a=h^70,c^b=cf,h^b=h^70,h^c=h^701456 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31907536, #1453×D71, C2×#22586638, … |
| maximal normal subgroup of | #31907536, #1453×D71, C2×#22586638, … |
| maximal quotient of | #31886823, #31886839, #31887883, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2808);