Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #2401 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D83 |
| commutator, socle, cosocle | C23×C83 | C24 |
| Fitting | #396×C83 | C2 |
| prime radical | C24×C83 | C23 |
| hypercenter | #396 | D83 |
| hypocenter | C83 | #2401 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #396 | |
432 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 139 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=fg,b^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^82,c^b=cg,h^b=h^82,h^d=h^82946 conjugacy classes — view the full character table.
| maximal subgroup of | #2401×D83, C2×#24910765, #35570714, … |
| maximal normal subgroup of | #2401×D83, C2×#24910765, #35570714, … |
| maximal quotient of | #35326102, #35326126, #35326181, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7812);