Finite Group DatabasebetaFinite Group Databasebeta| order | 16878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D97⋊C3 |
| unambiguous semidirect product | D97⋊(C3×C29) |
| unambiguous semidirect product | (C97⋊C3)⋊(C2×C29) |
| unambiguous semidirect product | (C29×D97)⋊C3 |
| Fitting, socle, Hall | C29×C97 ⋊ C2×C3 |
| derived, Sylow | C97 ⋊ C2×C3×C29 |
| Hall | C29×C97⋊C3 ⋊ C2 |
| Hall | C29×D97 ⋊ C3 |
| Hall | C97⋊C3 ⋊ C2×C29 |
| Hall | D97 ⋊ C3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D97⋊C3 |
| commutator, cosocle, hypocenter | C97 | C2×C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C29×C97 | C2×C3 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C29 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2813 |
638 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C29×#87604⋊C3, #26014561⋊C3, D29×D97⋊C3, … |
| maximal normal subgroup of | C29×#87604⋊C3, #26014561⋊C3, D29×D97⋊C3, … |
| maximal quotient of | C29×Dic97⋊C3, C2×C29×D97⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16878, 10);