Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D37×C49⋊C3 |
| Fitting, derived, Hall | C37×C49 ⋊ C2×C3 |
| Hall | C37×C49⋊C3 ⋊ C2 |
| Hall | C49×D37 ⋊ C3 |
| Sylow | C49 ⋊ C3×D37 |
| Sylow | C37 ⋊ C2×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C37×C49 | C2×C3 |
| Frattini | C7 | ΓL(1,𝔽8)×D37 |
| socle | C7×C37 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C37×C49 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
380 conjugacy classes — view the full character table.
| maximal subgroup of | (C49⋊C3)⋊#3866, D37×D49⋊C3, C49⋊C3×#3866, … |
| maximal normal subgroup of | (C49⋊C3)⋊#3866, D37×D49⋊C3, C49⋊C3×#3866, … |
| maximal quotient of | C49⋊C3×Dic37, C2×D37×C49⋊C3, D37×C49⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 5);