Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of C3⋊D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
| direct product | C32×C3⋊D21 |
| unambiguous semidirect product | C3⋊(C32×D21) |
| Fitting, socle, Hall | C34×C7 ⋊ C2 |
| derived | C32×C7 ⋊ C2×C32 |
| Sylow | C34 ⋊ D7 |
| Sylow | C7 ⋊ C32×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊D21 |
| commutator, cosocle, hypocenter | C32×C7 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C34×C7 | C2 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C32 | |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
297 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72249197, C3×C7⋊#4183, #72249200, … |
| maximal normal subgroup of | C32×C3⋊(C3⋊AGL(1,𝔽7)), C32×D7×C3⋊D3 |
| maximal quotient of | #72249199 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 249);