Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C71 ⋊ #1275 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic71 |
| commutator | C4×C71 | C4×C8 |
| Frattini | C2×C42 | C2×D71 |
| Fitting | C2×#97×C71 | C2 |
| socle | C22×C71 | #95 |
| hypercenter | C2×#97 | D71 |
| hypocenter | C71 | #1275 |
| LCS | G ▷ C4×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#97 | |
152 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=d,b^2=e,c^2=f,d^2=g,e^2=f,b^a=bc,e^a=ef,h^a=h^70,d^b=df1444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31884212, #31884213, #31884215, … |
| maximal normal subgroup of | #31884212, #31884213, #31884215, … |
| maximal quotient of | C71⋊#7014, #31883988, #31883990, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2341);