Finite Group DatabasebetaFinite Group Databasebeta| order | 10352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C647 ⋊ C2 |
| Sylow | C647 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D647 |
| commutator, socle, cosocle | C2×C647 | C23 |
| Fitting | Q8×C647 | C2 |
| hypercenter | Q8 | D647 |
| hypocenter | C647 | #41 |
| LCS | G ▷ C2×C647 ▷ C647 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,647|c^2=d,b^a=bd,e^a=e^646,e^b=e^646,e^c=e^6461625 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35208433, #35208435, #35208439, … |
| maximal normal subgroup of | #35208433, #35208435, #35208439, … |
| maximal quotient of | #35208370, #35208374, Q8×Dic647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10352, 41);