Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #568×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3586 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×D284 |
| commutator | C4×C71 | C25 |
| Frattini | C4 | C24×D71 |
| Fitting | #568×C71 | C2 |
| socle | C2×C71 | C23×D4 |
| hypercenter | #568 | D71 |
| hypocenter | C71 | #3586 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #568 | |
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|b^2=g,f^2=g,b^a=bf,e^a=eg,f^a=fg,h^a=h^70,f^b=fg,h^b=h^70,d^c=dg1231 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32028759, #32028760, #32028781, … |
| maximal normal subgroup of | #32028759, #32028760, #32028781, … |
| maximal quotient of | #32861030, #32861037, #32861137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 19298);