Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | #519×D83 |
| Fitting | #519×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D83 |
| commutator | C2×C83 | C24×C4 |
| Fitting | #519×C83 | C2 |
| socle, cosocle | C22×C83 | C25 |
| prime radical | C23×D83 | C23 |
| hypercenter | #519 | D83 |
| hypocenter | C83 | C2×#519 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ #519 | |
1488 conjugacy classes of subgroups; only the 813 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 813 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1830×D83, #1857×D83, #35405229, … |
| maximal normal subgroup of | #1830×D83, #1857×D83, #35405229, … |
| maximal quotient of | #2274×D83, #2276×D83, #35562651, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17698);