Finite Group DatabasebetaFinite Group Databasebeta| order | 21004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D59×D89 |
| unambiguous semidirect product | (C89×D59)⋊C2 |
| unambiguous semidirect product | (C59×D89)⋊C2 |
| unambiguous semidirect product | D5251⋊C2 |
| Fitting, socle, derived, Hall | C59×C89 ⋊ C22 |
| Sylow | C89 ⋊ C2×D59 |
| Sylow | C59 ⋊ C2×D89 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C59×C89 | C22 |
| LCS | G ▷ C59×C89 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5251 |
1426 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21004, 8);