Finite Group DatabasebetaFinite Group Databasebeta| order | 8436 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C19×C37 ⋊ C3×C4 |
| Hall | Dic703 ⋊ C3 |
| Hall | #14523721 ⋊ C4 |
| Sylow | C37 ⋊ (C19⋊C3)⋊C4 |
| Sylow | C19 ⋊ Dic37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #16862431 |
| commutator, hypocenter | C19×C37 | C3×C4 |
| Fitting, socle | C2×C19×C37 | C2×C3 |
| LCS | G ▷ C19×C37 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,19,37,2|a^2=e,c^a=c^18,d^a=d^36,c^b=c^7,d^b=d^10246 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8436, 24);