Finite Group DatabasebetaFinite Group Databasebeta| order | 16698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C11 |
| direct product | C23×(C11⋊D11)⋊C3 |
| unambiguous semidirect product | (C11⋊D11)⋊(C3×C23) |
| unambiguous semidirect product | (C23×C11⋊D11)⋊C3 |
| Fitting, socle, Hall | C112×C23 ⋊ C2×C3 |
| derived, Sylow | C112 ⋊ C2×C3×C23 |
| Hall | C23×C112⋊C3 ⋊ C2 |
| Hall | C23×C11⋊D11 ⋊ C3 |
| Hall | C112⋊C3 ⋊ C2×C23 |
| Hall | C11⋊D11 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | (C11⋊D11)⋊C3 |
| commutator, cosocle, hypocenter | C112 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C112×C23 | C2×C3 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C23 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 759 |
598 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16698, 24);