Finite Group DatabasebetaFinite Group Databasebeta| order | 12087 |
| isoclinism | isoclinic class of C79⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C17 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C17×C79 ⋊ C3 |
| derived, Sylow | C79 ⋊ C32×C17 |
| Hall | C17×C79 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | C79⋊C3 |
| commutator, cosocle, hypocenter | C79 | C32×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C79 | C3 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C3×C17 | |
24 conjugacy classes of subgroups.
1479 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C17×D79⋊C3, C3×C17⋊(D79⋊C3), C3×D17×C79⋊C3, … |
| maximal normal subgroup of | C3×C17×D79⋊C3, C3×C17⋊(D79⋊C3), C3×D17×C79⋊C3, … |
| maximal quotient of | C2×C3×C17×C79⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12087, 4);