Finite Group DatabasebetaFinite Group Databasebeta| order | 10212 |
| isoclinism | isoclinic class of #3866⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×#3866⋊C3 |
| unambiguous semidirect product | #3866⋊(C3×C23) |
| unambiguous semidirect product | (C23×#3866)⋊C3 |
| Fitting, socle, Hall | C23×C37 ⋊ C3×C4 |
| derived, Sylow | C37 ⋊ C3×C4×C23 |
| Hall | C23×#3866 ⋊ C3 |
| Hall | C23×C37⋊C3 ⋊ C4 |
| Hall | #3866 ⋊ C3×C23 |
| Hall | C37⋊C3 ⋊ C4×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #3866⋊C3 |
| commutator, hypocenter | C37 | C3×C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C37 | C3×C4 |
| prime radical | C23×D37⋊C3 | C2 |
| cosocle | D37 | C2×C3×C23 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
345 conjugacy classes — view the full character table.
| maximal subgroup of | C23×AGL(1,𝔽37), C3×C23×#3866⋊C3, C23×C3⋊(#3866⋊C3) |
| maximal normal subgroup of | C23×AGL(1,𝔽37), C3×C23×#3866⋊C3 |
| maximal quotient of | C23×#13050613, C3×C23×#3866⋊C3, C23×C3⋊(#3866⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10212, 14);