Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #493×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3292 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #17986634 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #493×C71 | C2 |
| socle | C2×C71 | D42 |
| hypercenter | #493 | D71 |
| hypocenter | C71 | #3292 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #493 | |
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,c^b=cg,d^b=de,e^b=eg,h^b=h^70,f^c=fg,h^c=h^70,e^d=eg,h^d=h^70799 conjugacy classes — view the full character table.
| maximal subgroup of | #31910843, #31910846, #31910853, … |
| maximal normal subgroup of | #31910843, #31910846, #31910853, … |
| maximal quotient of | #31988738, #31988840, #31988915, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 16309);