Finite Group DatabasebetaFinite Group Databasebeta| order | 16215 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C23 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C3×C5×C47 ⋊ C23 |
| derived, Sylow | C47 ⋊ C3×C5×C23 |
| Hall | C5×C47 ⋊ C3×C23 |
| Hall | C3×C47 ⋊ C5×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C47⋊C23 |
| commutator, cosocle, hypocenter | C47 | C3×C5×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C47 | C23 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C3×C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 705 |
375 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C5×C47⋊C23, C3×C5×AGL(1,𝔽47), C3×D5×C47⋊C23, … |
| maximal normal subgroup of | C2×C3×C5×C47⋊C23, C3×C5×AGL(1,𝔽47), C3×D5×C47⋊C23, … |
| maximal quotient of | C2×C3×C5×C47⋊C23 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16215, 2);