Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #1940 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D83 |
| commutator, socle, prime radical | C23×C83 | C22×C4 |
| Fitting | #336×C83 | C2 |
| cosocle | C22×C4×C83 | C23 |
| hypercenter | #336 | D83 |
| hypocenter | C83 | #1940 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
248 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 105 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=f,b^2=f,c^2=e,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^b=h^82,h^c=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1940×D83, C2×#24908185, #35407683, … |
| maximal normal subgroup of | #1940×D83, C2×#24908185, #35407683, … |
| maximal quotient of | #35302960, #35302965, #35302970, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5232);