Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | Q82×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3555 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D83 |
| commutator, socle, cosocle | C22×C83 | C25 |
| Fitting | Q82×C83 | C2 |
| prime radical | #14581767 | C22 |
| hypercenter | Q82 | D83 |
| hypocenter | C83 | #3555 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ Q82 | |
910 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^82,c^b=cg,d^b=df,h^d=h^821063 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35382491, #35382499, #35382506, … |
| maximal normal subgroup of | #35382491, #35382499, #35382506, … |
| maximal quotient of | #35567304, #35567425, #35567579, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 18999);