Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×Dic21 |
| derived, Hall | C3×C7 ⋊ C4×C8 |
| Sylow | C7 ⋊ C8×Dic3 |
| Sylow | C3 ⋊ C8×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D21 |
| commutator, hypocenter | C3×C7 | C4×C8 |
| Frattini | C2×C4 | C2×D21 |
| Fitting | C2×C3×C7×C8 | C2 |
| socle, prime radical | C22×C3×C7 | C2×C4 |
| cosocle | C2×C3×C4×C7 | C22 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C2×C8 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | #13050900, #13050903, #13050956, … |
| maximal normal subgroup of | #13050900, #13050903, #13050956, … |
| maximal quotient of | C8×C3⋊(C7⋊C8), #13051358, C16×Dic21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 234);