Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of D3×D72 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D3×D72 |
| unambiguous semidirect product | (D3×C7×D7)⋊C2 |
| unambiguous semidirect product | (D3×C7⋊D7)⋊C2 |
| unambiguous semidirect product | (D7×D21)⋊C2 |
| Fitting, socle, derived, Hall | C3×C72 ⋊ C23 |
| Sylow | C72 ⋊ C22×D3 |
| Sylow | C3 ⋊ C2×D72 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72 | C23 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 | |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 42 |
75 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#64423⋊C2, #72213616, D72×C3⋊D3, … |
| maximal normal subgroup of | D3×#64423⋊C2, C2×D3×D72, C3×D3×D72, … |
| maximal quotient of | #72213616, D3×#87639, D3×#87641, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 237);