Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #2732 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D83 |
| commutator, socle, cosocle | C23×C83 | C24 |
| Fitting | #390×C83 | C2 |
| prime radical | C22×D4×C83 | C22 |
| hypercenter | #390 | D83 |
| hypocenter | C83 | #2732 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #390 | |
528 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=ef,b^2=ef,d^2=ef,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^82,h^d=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35293105, #35293109, #35293206, … |
| maximal normal subgroup of | #35293105, #35293109, #35293206, … |
| maximal quotient of | #35332280, #35332401, #35332821, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 11527);