Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C37⋊C3)⋊D49 |
| Fitting, derived, Hall | C37×C49 ⋊ C2×C3 |
| Hall | C49×C37⋊C3 ⋊ C2 |
| Hall | D1813 ⋊ C3 |
| Hall | C37⋊C3 ⋊ D49 |
| Sylow | C49 ⋊ D37⋊C3 |
| Sylow | C37 ⋊ C3×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C37×C49 | C2×C3 |
| Frattini | C7 | (C37⋊C3)⋊D7 |
| socle | C7×C37 | C3×D7 |
| LCS | G ▷ C37×C49 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,37,7|c^7=e^6,c^a=c^6e,d^a=d^36,e^a=e^6,d^b=d^10372 conjugacy classes — view the full character table.
| maximal subgroup of | D49×D37⋊C3, C2×(C37⋊C3)⋊D49, #45657247, … |
| maximal normal subgroup of | D49×D37⋊C3, C2×(C37⋊C3)⋊D49, #45657247, … |
| maximal quotient of | #36344151, C2×(C37⋊C3)⋊D49, #66524⋊D49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 4);