Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| isoclinism | isoclinic class of D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C24×C4×D83 |
| Fitting | C24×C4×C83 ⋊ C2 |
| derived, Sylow | C83 ⋊ C25×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | D83 |
| commutator, hypocenter | C83 | C25×C4 |
| Frattini | C2 | C25×D83 |
| Fitting | C24×C4×C83 | C2 |
| socle | C25×C83 | C22 |
| prime radical | C25×D83 | C2 |
| cosocle | C2×C83 | C26 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C24×C4 | |
10552 conjugacy classes of subgroups.
2752 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊#95×D83, C2×(C2×D83)⋊#95, #35325609, … |
| maximal normal subgroup of | C22⋊#95×D83, C2×(C2×D83)⋊#95, #35325609, … |
| maximal quotient of | C23×C42×D83, C24×C4×Dic83, C23×C22⋊C4×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19299);