Finite Group DatabasebetaFinite Group Databasebeta| order | 21204 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C19×C31 ⋊ C4×C9 |
| Hall | #19127106 ⋊ C4 |
| Hall | Dic589 ⋊ C9 |
| Sylow | C31 ⋊ #4296⋊C4 |
| Sylow | C19 ⋊ Dic31⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #24902714 |
| commutator, hypocenter | C19×C31 | C4×C9 |
| Fitting, socle | C2×C19×C31 | C2×C9 |
| prime radical, cosocle | C2×C31×C19⋊C3 | C2×C3 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2356 |
Polycyclic presentation:
2,3^2,19,31,2|a^2=f,b^3=c,d^a=d^18,e^a=e^30,d^b=d^4,e^b=e^25,d^c=d^7128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21204, 68);