Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C172 ⋊ C4×C9 |
| Hall | #14579585 ⋊ C4 |
| Hall | #11923883 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C172 | C4×C9 |
| prime radical, cosocle | (C17⋊D17)⋊C3 | C2×C3 |
| LCS | G ▷ C172 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,3,17^2|a^2=c,b^3=d,e^a=e^13,f^a=f^13,e^b=e^2f^16,f^b=e^11f^12,e^c=e^16,f^c=f^16,e^d=e^2f^9,f^d=e^3f^1444 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 94);