Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | #379×D83 |
| Fitting | #379×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D83 |
| commutator | C22×C83 | C23×C4 |
| Fitting | #379×C83 | C2 |
| socle, cosocle | C23×C83 | C24 |
| prime radical | C25×D83 | C2 |
| hypercenter | #379 | D83 |
| hypocenter | C83 | C2×#379 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #379 | |
3464 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 365 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1304×D83, #35294727, #1316×D83, … |
| maximal normal subgroup of | #1304×D83, #35294727, #1316×D83, … |
| maximal quotient of | C22⋊#95×D83, #35325609, #379×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6876);