Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #520×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3428 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D83 |
| commutator | C2×C83 | C24×C4 |
| Fitting | #520×C83 | C2 |
| socle, cosocle | C22×C83 | C25 |
| prime radical | C2×#41×D83 | C2 |
| hypercenter | #520 | D83 |
| hypocenter | C83 | #3428 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ #520 | |
1540 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,e^2=f,b^a=bf,d^a=df,c^b=cf,h^d=h^82,h^e=h^821462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35405270, #35405272, #35405288, … |
| maximal normal subgroup of | #35405270, #35405272, #35405288, … |
| maximal quotient of | #35562617, #35562629, #35562632, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17710);