Finite Group DatabasebetaFinite Group Databasebeta| order | 6021 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C9×C223 ⋊ C3 |
| Sylow | C223 ⋊ 3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C223⋊C3 |
| commutator, socle | C3×C223 | C32 |
| Fitting | C9×C223 | C3 |
| hypercenter | C9 | C223⋊C3 |
| hypocenter | C223 | 3−1+2 |
| LCS | G ▷ C3×C223 ▷ C223 | |
| UCS | C1 ◁ C3 ◁ C9 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
3^3,223|a^3=c,b^a=bc,d^b=d^39677 conjugacy classes — view the full character table.
| maximal subgroup of | 3−1+2×C223⋊C3, C3×#20258261, #31825606, … |
| maximal normal subgroup of | 3−1+2×C223⋊C3, C3×#20258261, #31825606, … |
| maximal quotient of | (C3×C223⋊C3)⋊C9, (C223⋊C9)⋊C9, #31825580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6021, 11);