Finite Group DatabasebetaFinite Group Databasebeta| order | 882 |
| isoclinism | isoclinic class of C3⋊(C3⋊(C7⋊D7)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3×C7 |
| unambiguous semidirect product | C3⋊(C3⋊(C7⋊D7)) |
| unambiguous semidirect product | C7⋊(C3⋊D21) |
| Fitting, socle, derived, Hall | C32×C72 ⋊ C2 |
| Sylow | C72 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C72 | C2 |
| LCS | G ▷ C32×C72 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 441 |
Polycyclic presentation:
2,3^2,7^2|b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^6222 conjugacy classes — view the full character table.
| maximal subgroup of | #13183676, C3⋊D3×C7⋊D7, D7×C3⋊D21, … |
| maximal normal subgroup of | #13183676, C3⋊D3×C7⋊D7, D7×C3⋊D21, … |
| maximal quotient of | C3⋊(C3⋊(C7⋊Dic7)), C2×C3⋊(C3⋊(C7⋊D7)), C5×C3⋊(C3⋊(C7⋊D7)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(882, 67);