Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Fitting | C2×H(5,𝔽2)×C71 ⋊ C2 |
| Sylow | C71 ⋊ H(7,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C25×D71 |
| commutator, socle | C2×C71 | C26 |
| Fitting | C2×H(5,𝔽2)×C71 | C2 |
| hypercenter | C2×H(5,𝔽2) | D71 |
| hypocenter | C71 | H(7,𝔽2) |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C2×H(5,𝔽2) | |
5992 conjugacy classes of subgroups; only the 3201 normal subgroups are shown.
This group has 5992 conjugacy classes of subgroups — too many to draw. Only its 3201 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^a=bg,f^a=fg,e^b=eg,d^c=dg,h^f=h^701255 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32146194, #32146198, #32146208, … |
| maximal normal subgroup of | #32146194, #32146198, #32146208, … |
| maximal quotient of | #32904068, #32904069, #32904071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 19320);