Finite Group DatabasebetaFinite Group Databasebeta| order | 8214 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#16861551 |
| Fitting, socle, Hall | C2×C372 ⋊ C3 |
| derived, Sylow | C372 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #16861551 |
| commutator, hypocenter | C372 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C372 | C3 |
| LCS | G ▷ C372 | |
| UCS | C1 ◁ C2 | |
160 conjugacy classes of subgroups.
918 conjugacy classes — view the full character table.
| maximal subgroup of | #30656059, #30656060, C4×#16861551, … |
| maximal normal subgroup of | #30656059, #30656060, C4×#16861551, … |
| maximal quotient of | C4×#16861551, C22×#16861551, C2×#27134460, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8214, 17);