Finite Group DatabasebetaFinite Group Databasebeta| order | 10212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D23×D111 |
| unambiguous semidirect product | (C3×D23)⋊D37 |
| unambiguous semidirect product | (C37×D23)⋊D3 |
| Fitting, socle, derived, Hall | C3×C23×C37 ⋊ C22 |
| Hall | C23×C37 ⋊ C2×D3 |
| Hall | C3×C37 ⋊ C2×D23 |
| Hall | C3×C23 ⋊ C2×D37 |
| Sylow | C37 ⋊ D3×D23 |
| Sylow | C23 ⋊ C2×D111 |
| Sylow | C3 ⋊ D23×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C23×C37 | C22 |
| LCS | G ▷ C3×C23×C37 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
741 conjugacy classes — view the full character table.
| maximal subgroup of | D23×D333, D23×C3⋊(D37⋊C3), C3×D23×D111, … |
| maximal normal subgroup of | D23×C3⋊(D37⋊C3), C3×D23×D111 |
| maximal quotient of | D23×D333, C3×D23×D111, D69×D111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10212, 28);