Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #397×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2786 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D83 |
| commutator, socle, cosocle | C23×C83 | C24 |
| Fitting | #397×C83 | C2 |
| prime radical | C22×C22⋊D83 | C22 |
| hypercenter | #397 | D83 |
| hypocenter | C83 | #2786 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #397 | |
434 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=efg,b^2=f,d^2=ef,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^d=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #35612242, #35612257, #35612339, … |
| maximal normal subgroup of | #35612242, #35612257, #35612339, … |
| maximal quotient of | #35332261, #35332536, #35332693, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12219);