Finite Group DatabasebetaFinite Group Databasebeta| order | 16698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×#10624391 |
| Fitting, socle, Hall | C112×C23 ⋊ D3 |
| derived, Hall | C112⋊C3 ⋊ C2×C23 |
| Hall | C23×C112⋊C3 ⋊ C2 |
| Sylow | C112 ⋊ D3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #10624391 |
| commutator, cosocle, hypocenter | C112⋊C3 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C112×C23 | D3 |
| LCS | G ▷ C112⋊C3 | |
| UCS | C1 ◁ C23 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 759 |
874 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×#10624391, C23×#10624391⋊C2, #10624391⋊D23, … |
| maximal normal subgroup of | D23×#10624391, C23×#10624391⋊C2, #10624391⋊D23, … |
| maximal quotient of | C23×#13089712, C2×C23×#10624391 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16698, 22);