Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C71 ⋊ #1723 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14556124 |
| commutator | C42×C71 | C23 |
| Frattini | C42 | C22×D71 |
| Fitting | #500×C71 | C2 |
| socle | C22×C71 | #127 |
| hypercenter | #500 | D71 |
| hypocenter | C71 | #1723 |
| LCS | G ▷ C42×C71 ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #500 | |
176 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|a^2=g,b^2=d,c^2=eg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^70,c^b=cf,h^c=h^70796 conjugacy classes — view the full character table.
| maximal subgroup of | #1723×D71, C2×#22588018, #31985254, … |
| maximal normal subgroup of | #1723×D71, C2×#22588018, #31985254, … |
| maximal quotient of | #31891242, #31897266, #31897270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 4188);