Finite Group DatabasebetaFinite Group Databasebeta| order | 10212 |
| automorphism | Aut(G) order 8087904 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5106 |
| direct product | C2×D2553 |
| unambiguous semidirect product | (C2×C3)⋊D851 |
| unambiguous semidirect product | (C2×C23)⋊D111 |
| unambiguous semidirect product | (C2×C37)⋊D69 |
| Fitting, socle | C2×C3×C23×C37 ⋊ C2 |
| derived, Hall | C3×C23×C37 ⋊ C22 |
| Hall | C23×C37 ⋊ C2×D3 |
| Hall | C3×C37 ⋊ C2×D23 |
| Hall | C3×C23 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×D69 |
| Sylow | C23 ⋊ C2×D111 |
| Sylow | C3 ⋊ C2×D851 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2553 |
| commutator, cosocle, hypocenter | C3×C23×C37 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C23×C37 | C2 |
| LCS | G ▷ C3×C23×C37 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
2556 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D7659, C2×C3⋊(C23⋊(D37⋊C3)), D3×D2553, … |
| maximal normal subgroup of | C2×C3⋊(C23⋊(D37⋊C3)), C2×C3×D2553, D10212 |
| maximal quotient of | C2×D7659, D3×D2553, C2×C3×D2553, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10212, 34);