Finite Group DatabasebetaFinite Group Databasebeta| order | 17892 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×Dic213 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽8)×Dic71) |
| unambiguous semidirect product | C71⋊(Dic3×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×Dic213)⋊C3 |
| derived | C3×C7×C71 ⋊ C3×C4 |
| Hall | C3×ΓL(1,𝔽8)×C71 ⋊ C4 |
| Hall | C7×C71 ⋊ C3×Dic3 |
| Sylow | C71 ⋊ Dic3×ΓL(1,𝔽8) |
| Hall | C3×ΓL(1,𝔽8) ⋊ Dic71 |
| Sylow | C7 ⋊ C3×Dic213 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | ΓL(1,𝔽8)×D213 |
| commutator, hypocenter | C3×C7×C71 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C7×C71 | C2×C3 |
| prime radical | C2×C3×ΓL(1,𝔽8)×C71 | C2 |
| LCS | G ▷ C3×C7×C71 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5964 |
1080 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17892, 58);