Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C3⋊(C7⋊D259) |
| unambiguous semidirect product | C7⋊D777 |
| unambiguous semidirect product | C37⋊(C3⋊(C7⋊D7)) |
| Fitting, socle, derived, Hall | C3×C72×C37 ⋊ C2 |
| Hall | C72×C37 ⋊ D3 |
| Hall | C3×C72 ⋊ D37 |
| Hall | C3×C37 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D111 |
| Sylow | C37 ⋊ C3⋊(C7⋊D7) |
| Sylow | C3 ⋊ C7⋊D259 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C37 | C2 |
| LCS | G ▷ C3×C72×C37 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7^2,37|b^a=b^2,c^a=c^6,d^a=d^6,e^a=e^362721 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×D777, D21×D259, D37×C3⋊(C7⋊D7), … |
| maximal normal subgroup of | D7×D777, D21×D259, D37×C3⋊(C7⋊D7), … |
| maximal quotient of | C3⋊(C7⋊Dic259), C2×C3⋊(C7⋊D259), C7⋊D2331, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 90);