Finite Group DatabasebetaFinite Group Databasebeta| order | 8190 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D5×#11717942 |
| unambiguous semidirect product | C5⋊(C2×#11717942) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D5×#63271 |
| commutator, hypocenter | C5×C7×C13 | C2×C9 |
| Fitting, socle | C3×C5×C7×C13 | C2×C3 |
| LCS | G ▷ C5×C7×C13 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
396 conjugacy classes — view the full character table.
| maximal subgroup of | #30655022, #30655026, #30655034, … |
| maximal normal subgroup of | #30655022, #30655026, #30655034, … |
| maximal quotient of | Dic5×#11717942, C2×D5×#11717942 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8190, 36);