Finite Group DatabasebetaFinite Group Databasebeta| order | 37598 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D18799 |
| unambiguous semidirect product | C11⋊D1709 |
| unambiguous semidirect product | C1709⋊D11 |
| Fitting, socle, derived, Hall | C11×C1709 ⋊ C2 |
| Sylow | C1709 ⋊ D11 |
| Sylow | C11 ⋊ D1709 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C1709 | C2 |
| LCS | G ▷ C11×C1709 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1720 |
| transitive degree | μt(G) = 18799 |
A minimal faithful permutation representation — 2 generators on 1720 points:
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presentation:
2,11,1709|b^a=b^10,c^a=c^17089401 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37598, 3);