Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C71 ⋊ #3202 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D284 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #408×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #408 | D71 |
| hypocenter | C71 | #3202 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C2×#41 ◁ #408 | |
378 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 378 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|a^2=g,b^2=g,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^70,c^b=ce,d^b=dg,f^c=fg,h^c=h^701006 conjugacy classes — view the full character table.
| maximal subgroup of | #31909587, #31909590, #31909604, … |
| maximal normal subgroup of | #31909587, #31909590, #31909604, … |
| maximal quotient of | #32006560, #32007767, #32008765, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 15405);