Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×C3⋊C16 |
| unambiguous semidirect product | (C2×C3)⋊(C7×C16) |
| derived, Sylow | C3 ⋊ C2×C7×C16 |
| Hall | C3×C7 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7×C8 | D3 |
| commutator, hypocenter | C3 | C2×C7×C16 |
| Frattini | C8 | C2×D3×C7 |
| Fitting | C2×C3×C7×C8 | C2 |
| socle, prime radical | C22×C3×C7 | C8 |
| cosocle | C3×C8 | C22×C7 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C7×C8 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic7×C3⋊C16, #13050900, #13050901, … |
| maximal normal subgroup of | Dic7×C3⋊C16, #13050900, #13050901, … |
| maximal quotient of | C4×C7×C3⋊C16, C7×C4⋊(C3⋊C16), C2×C7×C3⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 191);