Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C22×#41×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3449 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D83 |
| commutator, socle, cosocle | C22×C83 | C25 |
| Frattini | C22 | C24×D83 |
| Fitting | C22×#41×C83 | C2 |
| hypercenter | C22×#41 | D83 |
| hypocenter | C83 | #3449 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C2×C4 ◁ C22×#41 | |
1556 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|e^2=f,b^a=bf,c^a=cg,d^a=df,c^b=cf,h^c=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35311039, #35311040, #35311058, … |
| maximal normal subgroup of | #35311039, #35311040, #35311058, … |
| maximal quotient of | #35562976, #35562980, #35563030, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17839);