Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C128 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C83⋊C128 |
| derived, Sylow | C83 ⋊ C128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C64 | D83 |
| commutator, hypocenter | C83 | C128 |
| Fitting, cosocle | C64×C83 | C2 |
| socle, prime radical | C2×C83 | C64 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C64 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^822752 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C128×D83, C2×C83⋊C128, #35292314, … |
| maximal normal subgroup of | C128×D83, C2×C83⋊C128, #35292314, … |
| maximal quotient of | C83⋊C256, C2×C83⋊C128 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2329);