Finite Group DatabasebetaFinite Group Databasebeta| order | 18315 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5×C37 · Schur multiplier (H2) = C3 |
| Fitting, socle, Hall | C32×C11×C37 ⋊ C5 |
| derived, Sylow | C11 ⋊ C32×C5×C37 |
| Hall | C11×C37 ⋊ C32×C5 |
| Hall | C32×C11 ⋊ C5×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C37 | C11⋊C5 |
| commutator, cosocle, hypocenter | C11 | C32×C5×C37 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C37 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C32×C37 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3663 |
2331 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C37×AGL(1,𝔽11), C32×C37⋊AGL(1,𝔽11), C32×C11⋊C5×D37, … |
| maximal normal subgroup of | C32×C37×AGL(1,𝔽11), C32×C37⋊AGL(1,𝔽11), C32×C11⋊C5×D37, … |
| maximal quotient of | C2×C32×C37×C11⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18315, 9);