Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C82×C71 ⋊ C2 |
| Sylow | C71 ⋊ #1335 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D568 |
| commutator | C8×C71 | C2×C8 |
| Frattini | C4×C8 | C2×D71 |
| Fitting | C82×C71 | C2 |
| socle | C2×C71 | D4⋊C8 |
| hypercenter | C82 | D71 |
| hypocenter | C71 | #1335 |
| LCS | G ▷ C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ C4×C8 ◁ C82 | |
100 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=d,c^2=eg,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^70,c^b=ce,e^b=eg,h^b=h^702284 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1335×D71, C2×#22586314, #31907237, … |
| maximal normal subgroup of | #1335×D71, C2×#22586314, #31907237, … |
| maximal quotient of | #31884102, #31884105, #31884120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2484);