Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C17 |
No aliases for this group.
| Fitting, socle, Sylow | C172 ⋊ Dic9 |
| derived, Hall | #14579585 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | #14579585 | C4 |
| Fitting, socle | C172 | Dic9 |
| prime radical | (C17⋊D17)⋊C3 | D3 |
| cosocle | #19104523 | C2 |
| LCS | G ▷ #14579585 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,17^2|a^2=b,c^3=d,c^a=c^2d^2,d^a=d^2,e^a=e^3f^4,f^a=e^6f^14,e^b=e^16,f^b=f^16,e^c=e^7f^11,f^c=e^9f^7,e^d=e^8f^3,f^d=e^4f^820 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 93);