Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | #14579583 ⋊ C4 |
| Sylow | C172 ⋊ Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19104513 |
| commutator, hypocenter | #14579583 | C4 |
| Frattini | C2×C3 | #13181892 |
| Fitting, socle, prime radical | C2×C3×C172 | D3 |
| cosocle | C2×#14579583 | C2 |
| LCS | G ▷ #14579583 | |
| UCS | C1 ◁ C2 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,17^2,2,3|a^2=e,b^3=f^2,b^a=b^2f,c^a=cd,d^a=d^16,f^a=f^2,c^b=c^14d^2,d^b=c^5d^2348 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 38);