Finite Group DatabasebetaFinite Group Databasebeta| order | 21777 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#13046197 |
| Fitting, socle, Hall | C7×C17×C61 ⋊ C3 |
| derived, Hall | C7×C61 ⋊ C3×C17 |
| Hall | C17×C61 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C17 ⋊ C61⋊C3 |
| Sylow | C61 ⋊ C17×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C17×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #13046197 |
| commutator, cosocle, hypocenter | C7×C61 | C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C61 | C3 |
| LCS | G ▷ C7×C61 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7259 |
2465 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21777, 4);