Finite Group DatabasebetaFinite Group Databasebeta| order | 10212 |
| isoclinism | isoclinic class of D111 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | C2×C23×D111 |
| unambiguous semidirect product | (C2×C3)⋊(C23×D37) |
| unambiguous semidirect product | (C2×C37)⋊(D3×C23) |
| Fitting, socle | C2×C3×C23×C37 ⋊ C2 |
| derived, Hall | C3×C37 ⋊ C22×C23 |
| Hall | C3×C23×C37 ⋊ C22 |
| Hall | C23×C37 ⋊ C2×D3 |
| Hall | C3×C23 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×D3×C23 |
| Sylow | C3 ⋊ C2×C23×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D111 |
| commutator, cosocle, hypocenter | C3×C37 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C23×C37 | C2 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C2×C23 | |
40 conjugacy classes of subgroups.
2622 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C23×D333, C2×C23×C3⋊(D37⋊C3), D3×C23×D111, … |
| maximal normal subgroup of | C2×C23×C3⋊(D37⋊C3), C2×C3×C23×D111 |
| maximal quotient of | C2×C23×D333, D3×C23×D111, C2×C3×C23×D111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10212, 36);