Finite Group DatabasebetaFinite Group Databasebeta| order | 18315 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5×C11 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C5×C11×C37 ⋊ C3 |
| derived, Sylow | C37 ⋊ C32×C5×C11 |
| Hall | C5×C11×C37 ⋊ C32 |
| Hall | C11×C37 ⋊ C32×C5 |
| Hall | C5×C37 ⋊ C32×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C11 | C37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C32×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C11×C37 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3×C5×C11 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6105 |
2475 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×C11×D37⋊C3, C3×C5×C11⋊(D37⋊C3), C3×C5×D11×C37⋊C3, … |
| maximal normal subgroup of | C3×C5×C11×D37⋊C3, C3×C5×C11⋊(D37⋊C3), C3×C5×D11×C37⋊C3, … |
| maximal quotient of | C2×C3×C5×C11×C37⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18315, 10);