Finite Group DatabasebetaFinite Group Databasebeta| order | 828 |
| isoclinism | isoclinic class of D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic69 |
| unambiguous semidirect product | C3⋊(C3×Dic23) |
| unambiguous semidirect product | C23⋊(C3×Dic3) |
| derived | C3×C23 ⋊ C3×C4 |
| Hall | C32×C23 ⋊ C4 |
| Sylow | C23 ⋊ C3×Dic3 |
| Sylow | C32 ⋊ Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D69 |
| commutator, hypocenter | C3×C23 | C3×C4 |
| Frattini | C2 | C3×D69 |
| Fitting, socle, prime radical | C2×C32×C23 | C2 |
| cosocle | C2×C3×C23 | C2×C3 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C2×C3 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 276 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic3×D23, C3×D3×Dic23, C3×#10587770, … |
| maximal normal subgroup of | C3×Dic3×D23, C3×D3×Dic23, C3×#10587770, … |
| maximal quotient of | C3×C3⋊(C23⋊C8), C2×C3×Dic69, C3×C5×Dic69, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(828, 13);