Finite Group DatabasebetaFinite Group Databasebeta| order | 10830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C5×#11762245 |
| Fitting, socle, Hall | C2×C5×C192 ⋊ C3 |
| derived, Sylow | C192 ⋊ C2×C3×C5 |
| Hall | C5×C192 ⋊ C2×C3 |
| Hall | C2×C192 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #11762245 |
| commutator, cosocle, hypocenter | C192 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C192 | C3 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C2×C5 | |
176 conjugacy classes of subgroups.
1230 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#16864558, C5×#16864560, #36343136, … |
| maximal normal subgroup of | C5×#16864558, C5×#16864560, #36343136, … |
| maximal quotient of | C4×C5×#11762245, C22×C5×#11762245, C2×C5×#15692429, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10830, 42);