Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| isoclinism | isoclinic class of #4296 |
| automorphism | ? |
| homology | Abelianization (H1) = C93 · Schur multiplier (H2) = C93 |
| direct product | C92×#4296 |
| Fitting | C92×C19 ⋊ C9 |
| derived, Sylow | C19 ⋊ C93 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C92 | #4296 |
| commutator, hypocenter | C19 | C93 |
| Frattini | C32 | C32×#4296 |
| Fitting | C92×C19 | C9 |
| socle | C32×C19 | C32×C9 |
| prime radical, cosocle | C32×C19⋊C3 | C33 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C92 | |
890 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 4204);