Finite Group DatabasebetaFinite Group Databasebeta| order | 49506 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C37×C223 ⋊ C2×C3 |
| Hall | #37613251 ⋊ C2 |
| Hall | D8251 ⋊ C3 |
| Sylow | C223 ⋊ D37⋊C3 |
| Sylow | C37 ⋊ D223⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C223 | C2×C3 |
| LCS | G ▷ C37×C223 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,37,223|c^a=c^36,d^a=d^222,c^b=c^26,d^b=d^1831381 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(49506, 28);