Finite Group DatabasebetaFinite Group Databasebeta| order | 8124 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#14582142 |
| Fitting, socle, Hall | C3×C677 ⋊ C4 |
| derived, Sylow | C677 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #14582142 |
| commutator, hypocenter | C677 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C677 | C4 |
| LCS | G ▷ C677 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
519 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#14582142, C32×#14582142, C3×C3⋊#14582142 |
| maximal normal subgroup of | C9×#14582142, C32×#14582142 |
| maximal quotient of | C9×#14582142, C32×#14582142, C3×C3⋊#14582142 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8124, 6);