Finite Group DatabasebetaFinite Group Databasebeta| order | 21417 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C59 · Schur multiplier (H2) = C11 |
| direct product | C59×C112⋊C3 |
| unambiguous semidirect product | C112⋊(C3×C59) |
| unambiguous semidirect product | (C112×C59)⋊C3 |
| Fitting, socle, Hall | C112×C59 ⋊ C3 |
| derived, Sylow | C112 ⋊ C3×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | C112⋊C3 |
| commutator, cosocle, hypocenter | C112 | C3×C59 |
| Frattini | C1 | G |
| Fitting, socle | C112×C59 | C3 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C59 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1947 |
2537 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21417, 3);