Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| isoclinism | isoclinic class of D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C64×D83 |
| Fitting | C64×C83 ⋊ C2 |
| derived, Sylow | C83 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C64 | D83 |
| commutator, hypocenter | C83 | C2×C64 |
| Frattini | C32 | C2×D83 |
| Fitting | C64×C83 | C2 |
| socle | C2×C83 | C2×C32 |
| prime radical | C2×D83 | C32 |
| cosocle | C32×C83 | C22 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C64 | |
40 conjugacy classes of subgroups.
2752 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C128×D83, #35292314, C2×C64×D83, … |
| maximal normal subgroup of | C128×D83, #35292314, C2×C64×D83, … |
| maximal quotient of | C64×Dic83, (C2×D83)⋊C64, Dic83⋊C64, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2718);