Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×#41×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3480 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D71 |
| commutator, socle | C22×C71 | C25 |
| Frattini | C22 | C24×D71 |
| Fitting | C4×#41×C71 | C2 |
| hypercenter | C4×#41 | D71 |
| hypocenter | C71 | #3480 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ C4×#41 | |
1112 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=g,b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,h^a=h^70,d^b=df,h^d=h^701450 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31964333, #31964339, #31964392, … |
| maximal normal subgroup of | #31964333, #31964339, #31964392, … |
| maximal quotient of | #32156843, Q8×#14556085, #32156885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 18108);