Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| isoclinism | isoclinic class of D3×#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | D3×#1057 |
| derived, Hall | C3×C13 ⋊ C2×C8 |
| Sylow | C13 ⋊ D3×C8 |
| Sylow | C3 ⋊ C2×#1057 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×#261 |
| commutator, hypocenter | C3×C13 | C2×C8 |
| Fitting, socle | C2×C3×C13 | C2×C4 |
| prime radical | C2×D3×C13 | C4 |
| cosocle | C3×Dic13 | C22 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
42 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D13⋊C8, #11929082, D3×#6118, … |
| maximal normal subgroup of | D3×D13⋊C8, #11929082, D3×#6118, … |
| maximal quotient of | D3×#6092, #11928212, Dic3×#1057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 127);