Finite Group DatabasebetaFinite Group Databasebeta| order | 13938 |
| isoclinism | isoclinic class of D101 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C3×C23×D101 |
| unambiguous semidirect product | C101⋊(C2×C3×C23) |
| Fitting, socle, Hall | C3×C23×C101 ⋊ C2 |
| derived, Sylow | C101 ⋊ C2×C3×C23 |
| Hall | C23×C101 ⋊ C2×C3 |
| Hall | C3×C101 ⋊ C2×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | D101 |
| commutator, cosocle, hypocenter | C101 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C101 | C2 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C3×C23 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6969 |
3588 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C23×#87938, C3×C23⋊#87938, C3×D23×D101, … |
| maximal normal subgroup of | C3×C23×#87938, C3×C23⋊#87938, C3×D23×D101, … |
| maximal quotient of | C3×C23×Dic101, C2×C3×C23×D101 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13938, 2);