Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #578×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3584 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D4×D83 |
| commutator, cosocle | C4×C83 | C25 |
| Frattini | C4 | C24×D83 |
| Fitting | #578×C83 | C2 |
| socle | C2×C83 | C23×D4 |
| hypercenter | #578 | D83 |
| hypocenter | C83 | #3584 |
| LCS | G ▷ C4×C83 ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #578 | |
1424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|e^2=g,f^2=g,b^a=bf,f^a=fg,f^b=fg,d^c=dg,h^c=h^82,h^d=h^82,h^e=h^82946 conjugacy classes — view the full character table.
| maximal subgroup of | #35558357, #35558363, #35558386, … |
| maximal normal subgroup of | #35558357, #35558363, #35558386, … |
| maximal quotient of | #36267966, #36268081, #36268520, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19280);