Finite Group DatabasebetaFinite Group Databasebeta| order | 20847 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C6949⋊C3 |
| Fitting, socle, derived, Sylow | C6949 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C6949 | C3 |
| LCS | G ▷ C6949 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 6949 |
| transitive degree | μt(G) = 6949 |
A minimal faithful permutation representation — 2 generators on 6949 points:
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presentation:
3,6949|b^a=b^19422319 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20847, 1);