Finite Group DatabasebetaFinite Group Databasebeta| order | 15318 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C37 · Schur multiplier (H2) = C3 |
| direct product | C32×C37×D23 |
| unambiguous semidirect product | C23⋊(C2×C32×C37) |
| Fitting, socle, Hall | C32×C23×C37 ⋊ C2 |
| derived, Sylow | C23 ⋊ C2×C32×C37 |
| Hall | C23×C37 ⋊ C2×C32 |
| Hall | C32×C23 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C37 | D23 |
| commutator, cosocle, hypocenter | C23 | C2×C32×C37 |
| Frattini | C1 | G |
| Fitting, socle | C32×C23×C37 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C32×C37 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7659 |
4329 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D23×D37, C3×D3×C37×D23, C3×D23×D111, … |
| maximal normal subgroup of | C32×D23×D37, C3×D3×C37×D23, C3×D23×D111, … |
| maximal quotient of | C32×C37×Dic23, C2×C32×C37×D23 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15318, 35);