Finite Group DatabasebetaFinite Group Databasebeta| order | 15165 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C5×C337 ⋊ C3 |
| derived, Sylow | C337 ⋊ C32×C5 |
| Hall | C5×C337 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C337⋊C3 |
| commutator, cosocle, hypocenter | C337 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C337 | C3 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C3×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5055 |
1725 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D337⋊C3, C3×C5⋊(D337⋊C3), C3×D5×C337⋊C3, … |
| maximal normal subgroup of | C3×C5×D337⋊C3, C3×C5⋊(D337⋊C3), C3×D5×C337⋊C3, … |
| maximal quotient of | C2×C3×C5×C337⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15165, 4);