Finite Group DatabasebetaFinite Group Databasebeta| order | 16878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C29⋊(D97⋊C3) |
| unambiguous semidirect product | (C97⋊C3)⋊D29 |
| unambiguous semidirect product | D2813⋊C3 |
| Fitting, socle, derived, Hall | C29×C97 ⋊ C2×C3 |
| Hall | C29×C97⋊C3 ⋊ C2 |
| Hall | D2813 ⋊ C3 |
| Hall | C97⋊C3 ⋊ D29 |
| Sylow | C97 ⋊ C3×D29 |
| Sylow | C29 ⋊ D97⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C97 | C2×C3 |
| LCS | G ▷ C29×C97 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2813 |
Polycyclic presentation:
2,3,29,97|c^a=c^28,d^a=d^96,d^b=d^35512 conjugacy classes — view the full character table.
| maximal subgroup of | #26014558⋊C3, #26014559⋊C3, D29×D97⋊C3, … |
| maximal normal subgroup of | #26014558⋊C3, #26014559⋊C3, D29×D97⋊C3, … |
| maximal quotient of | Dic2813⋊C3, C2×C29⋊(D97⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16878, 12);