Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #552×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3521 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D83 |
| commutator, socle, cosocle | C22×C83 | C25 |
| Fitting | #552×C83 | C2 |
| hypercenter | #552 | D83 |
| hypocenter | C83 | #3521 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ #552 | |
1042 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|c^2=f,e^2=fg,b^a=bf,c^a=cg,e^a=ef,h^a=h^82,d^b=df,h^b=h^82,h^c=h^82,h^d=h^82,h^e=h^821069 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36287083, #36287099, #36287110, … |
| maximal normal subgroup of | #36287083, #36287099, #36287110, … |
| maximal quotient of | #35564633, #35565141, #35565179, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 18585);