Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C13 · Schur multiplier (H2) = C4 |
| direct product | C4×Dic3×C13 |
| unambiguous semidirect product | C3⋊(C42×C13) |
| derived, Sylow | C3 ⋊ C42×C13 |
| Hall | C3×C13 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C13 | D3 |
| commutator, hypocenter | C3 | C42×C13 |
| Frattini | C22 | C2×D3×C13 |
| Fitting | C2×C3×C4×C13 | C2 |
| socle, prime radical | C22×C3×C13 | C22 |
| cosocle | C22×C3 | C22×C13 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C4×C13 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 624 |
312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3×#1055, #11927961, #11927985, … |
| maximal normal subgroup of | Dic3×#1055, #11927961, #11927985, … |
| maximal quotient of | C4×C13×C3⋊C8, C13×#803, C8×Dic3×C13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 84);