Finite Group DatabasebetaFinite Group Databasebeta| order | 18879 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C1 |
| Fitting, socle, derived, Hall | C29×C31 ⋊ C3×C7 |
| Hall | C31×C29⋊C7 ⋊ C3 |
| Hall | C29×C31⋊C3 ⋊ C7 |
| Sylow | C31 ⋊ C3×C29⋊C7 |
| Sylow | C29 ⋊ C7×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C31 | C3×C7 |
| LCS | G ▷ C29×C31 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 899 |
143 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C31⋊C3×C29⋊C7, D31⋊C3×C29⋊C7, C31⋊C3×D29⋊C7, … |
| maximal normal subgroup of | C2×C31⋊C3×C29⋊C7, D31⋊C3×C29⋊C7, C31⋊C3×D29⋊C7, … |
| maximal quotient of | C2×C31⋊C3×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18879, 7);