Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #504×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3407 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C23×D83 |
| commutator, socle | C2×C83 | C23×C8 |
| Fitting | #504×C83 | C2 |
| prime radical | #41×D83 | C4 |
| cosocle | C8×C83 | C24 |
| hypercenter | #504 | D83 |
| hypocenter | C83 | #3407 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C8 ◁ #504 | |
360 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 209 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=e,e^2=f,f^2=g,d^a=dg,c^b=cg,h^d=h^821708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35557647, #35557650, #35557654, … |
| maximal normal subgroup of | #35557647, #35557650, #35557654, … |
| maximal quotient of | #35557042, #35557052, #35557053, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17611);