Finite Group DatabasebetaFinite Group Databasebeta| order | 39402 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived | C3×C199 ⋊ C2×C3×C11 |
| Hall | C3×(C199⋊C3)⋊C11 ⋊ C2 |
| Hall | C3⋊(D199⋊C3) ⋊ C11 |
| Hall | C199⋊C11 ⋊ C3×D3 |
| Hall | C3×C199⋊C3 ⋊ C2×C11 |
| Sylow | C199 ⋊ C3×D3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C199 | C2×C3×C11 |
| LCS | G ▷ C3×C199 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,11,3,199|d^a=d^2,e^a=e^198,e^b=e^92,e^c=e^125108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(39402, 23);