Finite Group DatabasebetaFinite Group Databasebeta| order | 16698 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C112 · Schur multiplier (H2) = C11 |
| direct product | C3×C112×D23 |
| Fitting, socle, Hall | C3×C112×C23 ⋊ C2 |
| derived, Sylow | C23 ⋊ C2×C3×C112 |
| Hall | C112×C23 ⋊ C2×C3 |
| Hall | C3×C23 ⋊ C2×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C112 | D23 |
| commutator, cosocle, hypocenter | C23 | C2×C3×C112 |
| Frattini | C1 | G |
| Fitting, socle | C3×C112×C23 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C3×C112 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8349 |
4719 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×D11×D23, C3×D23×C11⋊D11, D3×C112×D23, … |
| maximal normal subgroup of | C3×C11×D11×D23, C3×D23×C11⋊D11, D3×C112×D23, … |
| maximal quotient of | C3×C112×Dic23, C2×C3×C112×D23 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16698, 38);