Finite Group DatabasebetaFinite Group Databasebeta| order | 10212 |
| isoclinism | isoclinic class of C22⋊(C37⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C23 · Schur multiplier (H2) = C2 |
| Fitting, socle, Hall | C22×C23×C37 ⋊ C3 |
| derived, Hall | C22×C37 ⋊ C3×C23 |
| Hall | C23×C37 ⋊ A4 |
| Hall | C22×C23 ⋊ C37⋊C3 |
| Sylow | C37 ⋊ A4×C23 |
| Sylow | C22 ⋊ C23×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C22⋊(C37⋊C3) |
| commutator, cosocle, hypocenter | C22×C37 | C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C22×C23×C37 | C3 |
| LCS | G ▷ C22×C37 | |
| UCS | C1 ◁ C23 | |
20 conjugacy classes of subgroups.
1196 conjugacy classes. The character table is too large to display.
| maximal subgroup of | A4×C23×C37⋊C3, C3×C23×C22⋊(C37⋊C3) |
| maximal normal subgroup of | A4×C23×C37⋊C3, C3×C23×C22⋊(C37⋊C3) |
| maximal quotient of | C23×C22⋊#66524, C3×C23×C22⋊(C37⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10212, 31);