Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #459×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3284 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D71 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #459×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #459 | D71 |
| hypocenter | C71 | #3284 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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=g,c^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^70,d^b=de,e^b=eg,h^b=h^70,h^c=h^70,e^d=eg700 conjugacy classes — view the full character table.
| maximal subgroup of | #31986857, #31986865, #31986872, … |
| maximal normal subgroup of | #31986857, #31986865, #31986872, … |
| maximal quotient of | #31988236, #31988251, #31988266, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 16243);