Finite Group DatabasebetaFinite Group Databasebeta| order | 10352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊Dic647 |
| Sylow | C647 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D647 |
| commutator | C2×C647 | C2×C4 |
| Fitting, prime radical | C23×C647 | C2 |
| socle, cosocle | C22×C647 | C22 |
| hypercenter | C23 | D647 |
| hypocenter | C647 | C22⋊C4 |
| LCS | G ▷ C2×C647 ▷ C647 | |
| UCS | C1 ◁ C22 ◁ C23 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,647|a^2=d,b^a=bc,e^a=e^6462594 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35208326, #35208327, C22⋊C4×D647, … |
| maximal normal subgroup of | #35208326, #35208327, C22⋊C4×D647, … |
| maximal quotient of | C647⋊#95, C22⋊(C647⋊C8), #35208327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10352, 18);