Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊(C7⋊C16) |
| unambiguous semidirect product | (C2×C3)⋊(C7⋊C16) |
| unambiguous semidirect product | (C2×C7)⋊(C3⋊C16) |
| derived, Hall | C3×C7 ⋊ C2×C16 |
| Sylow | C7 ⋊ C2×C3⋊C16 |
| Sylow | C3 ⋊ C2×C7⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D21 |
| commutator, hypocenter | C3×C7 | C2×C16 |
| Frattini | C8 | C2×D21 |
| Fitting | C2×C3×C7×C8 | C2 |
| socle, prime radical | C22×C3×C7 | C8 |
| cosocle | C3×C7×C8 | C22 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C2×C8 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | Dic7×C3⋊C16, Dic3×C7⋊C16, #13050901, … |
| maximal normal subgroup of | Dic7×C3⋊C16, Dic3×C7⋊C16, #13050901, … |
| maximal quotient of | C4×C3⋊(C7⋊C16), C4⋊(C3⋊(C7⋊C16)), C2×C3⋊(C7⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 232);