Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| isoclinism | isoclinic class of D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C22×C42×D83 |
| Fitting | C22×C42×C83 ⋊ C2 |
| derived, Sylow | C83 ⋊ C23×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C42 | D83 |
| commutator, hypocenter | C83 | C23×C42 |
| Frattini | C22 | C24×D83 |
| Fitting | C22×C42×C83 | C2 |
| socle | C24×C83 | C23 |
| prime radical | C24×D83 | C22 |
| cosocle | C22×C83 | C25 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C22×C42 | |
3000 conjugacy classes of subgroups.
2752 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35309620, #35309644, C4×#95×D83, … |
| maximal normal subgroup of | #35309620, #35309644, C4×#95×D83, … |
| maximal quotient of | C2×C43×D83, C22×C42×Dic83, C22×#95×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17664);