Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | #14579585 ⋊ C4 |
| Sylow | C172 ⋊ Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #19104522 |
| commutator, hypocenter | #14579585 | C4 |
| Fitting, socle | C2×C172 | D9 |
| prime radical | C2×C172⋊C3 | D3 |
| cosocle | C2×#14579585 | C2 |
| LCS | G ▷ #14579585 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,17^2,2|a^2=f,b^3=c,b^a=b^2c^2,c^a=c^2,e^a=de^16,d^b=d^12e^6,e^b=d^16e,d^c=d^14e^5,e^c=d^2e^292 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 74);