Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of C3⋊(C7⋊D7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C7 |
| direct product | C4×C3⋊(C7⋊D7) |
| Fitting | C3×C4×C72 ⋊ C2 |
| derived, Hall | C3×C72 ⋊ C2×C4 |
| Sylow | C72 ⋊ C4×D3 |
| Sylow | C3 ⋊ C4×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C3⋊(C7⋊D7) |
| commutator, hypocenter | C3×C72 | C2×C4 |
| Frattini | C2 | C2×C3⋊(C7⋊D7) |
| Fitting | C3×C4×C72 | C2 |
| socle, cosocle | C2×C3×C72 | C22 |
| prime radical | C2×C3⋊(C7⋊D7) | C2 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C4 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 588 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D3×C7⋊D7, C2×C4×C3⋊(C7⋊D7), D4×C3⋊(C7⋊D7), … |
| maximal normal subgroup of | C4×D3×C7⋊D7, C2×C4×C3⋊(C7⋊D7), D4×C3⋊(C7⋊D7), … |
| maximal quotient of | C2×C4×C3⋊(C7⋊D7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 205);