Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #563×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3559 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D83 |
| commutator, socle, cosocle | C22×C83 | C25 |
| Fitting | #563×C83 | C2 |
| hypercenter | #563 | D83 |
| hypocenter | C83 | #3559 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ #563 | |
1024 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=f,c^2=f,d^2=g,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^82,c^b=cg,d^b=df,h^c=h^82,h^e=h^82817 conjugacy classes — view the full character table.
| maximal subgroup of | #35385837, #35385846, #35385895, … |
| maximal normal subgroup of | #35385837, #35385846, #35385895, … |
| maximal quotient of | #35567354, #35567411, #35567643, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19047);