Finite Group DatabasebetaFinite Group Databasebeta| order | 19950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×ΓL(1,𝔽8)⋊D19 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C52×D19) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | ΓL(1,𝔽8)⋊D19 |
| commutator, cosocle, hypocenter | C7×C19 | C2×C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C19 | C2×C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C52 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3325 |
1300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19950, 56);