Finite Group DatabasebetaFinite Group Databasebeta| order | 21004 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C89 · Schur multiplier (H2) = C1 |
| direct product | C89×Dic59 |
| unambiguous semidirect product | C59⋊(C4×C89) |
| derived, Sylow | C59 ⋊ C4×C89 |
| Hall | C59×C89 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C89 | D59 |
| commutator, hypocenter | C59 | C4×C89 |
| Frattini | C2 | C89×D59 |
| Fitting, socle, prime radical | C2×C59×C89 | C2 |
| cosocle | C2×C59 | C2×C89 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C2×C89 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21004 |
5518 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21004, 2);