Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2396 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D71 |
| commutator, socle | C23×C71 | C24 |
| Frattini | C23 | C23×D71 |
| Fitting | C4×C4⋊C4×C71 | C2 |
| hypercenter | C4×C4⋊C4 | D71 |
| hypocenter | C71 | #2396 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C4⋊C4 | |
528 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^70,h^c=h^701444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31892540, #31892545, #31969732, … |
| maximal normal subgroup of | #31892540, #31892545, #31969732, … |
| maximal quotient of | #31919165, #31919179, #31919197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 7782);