Finite Group DatabasebetaFinite Group Databasebeta| order | 9804 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C19×C43 ⋊ C3×C4 |
| Hall | Dic817 ⋊ C3 |
| Hall | #14578575 ⋊ C4 |
| Sylow | C43 ⋊ (C19⋊C3)⋊C4 |
| Sylow | C19 ⋊ (C43⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #19096734 |
| commutator, hypocenter | C19×C43 | C3×C4 |
| Fitting, socle, cosocle | C2×C19×C43 | C2×C3 |
| prime radical | C2×#14578575 | C2 |
| LCS | G ▷ C19×C43 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,19,43,2|a^2=e,c^a=c^18,d^a=d^42,c^b=c^7,d^b=d^6284 conjugacy classes — view the full character table.
| maximal subgroup of | (C19⋊C3)⋊((C43⋊C3)⋊C4), C3×#23753935, C3⋊#23753935 |
| maximal normal subgroup of | (C19⋊C3)⋊((C43⋊C3)⋊C4), C3×#23753935 |
| maximal quotient of | #44440862, C3×#23753935, C3⋊#23753935 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9804, 24);