Finite Group DatabasebetaFinite Group Databasebeta| order | 18988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D47×D101 |
| unambiguous semidirect product | (D47×C101)⋊C2 |
| unambiguous semidirect product | (C47×D101)⋊C2 |
| unambiguous semidirect product | D4747⋊C2 |
| Fitting, socle, derived, Hall | C47×C101 ⋊ C22 |
| Sylow | C101 ⋊ C2×D47 |
| Sylow | C47 ⋊ C2×D101 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C47×C101 | C22 |
| LCS | G ▷ C47×C101 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4747 |
1300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18988, 8);