Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | H(3,𝔽4)×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3532 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D71 |
| commutator, socle | C22×C71 | C25 |
| Fitting | H(3,𝔽4)×C71 | C2 |
| hypercenter | H(3,𝔽4) | D71 |
| hypocenter | C71 | #3532 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
1336 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|b^a=bf,c^a=cg,d^a=dg,e^a=ef,c^b=cg,d^b=df,h^b=h^70,h^c=h^70,h^e=h^70703 conjugacy classes — view the full character table.
| maximal subgroup of | #32151508, #3532×D71, C2×#22602497, … |
| maximal normal subgroup of | #32151508, #3532×D71, C2×#22602497, … |
| maximal quotient of | #32160179, #32160808, #32160834, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 18667);