Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C17 |
No aliases for this group.
| derived, Sylow | C172 ⋊ C4×C9 |
| Hall | #14579585 ⋊ C4 |
| Hall | #11923880 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #19104523 |
| commutator, hypocenter | C172 | C4×C9 |
| Fitting, socle | C2×C172 | C2×C9 |
| prime radical, cosocle | C2×C172⋊C3 | C2×C3 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,17^2,2|a^2=f,b^3=c,d^a=d^16,e^a=e^16,d^b=d^2e^16,e^b=d^11e^12,d^c=d^2e^9,e^c=d^3e^1468 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 75);