Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #525×C83 ⋊ C2 |
| Sylow | C83 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D83 |
| commutator, socle, cosocle | C22×C83 | C25 |
| Frattini | C22 | C24×D83 |
| Fitting | #525×C83 | C2 |
| hypercenter | #525 | D83 |
| hypocenter | C83 | D4×#41 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
1648 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|e^2=f,b^a=bf,c^a=cg,d^b=df,h^d=h^821198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35420073, #35420076, #35420084, … |
| maximal normal subgroup of | #35420073, #35420076, #35420084, … |
| maximal quotient of | #35563602, #35563605, #35563718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17993);