Finite Group DatabasebetaFinite Group Databasebeta| order | 11655 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C3×C5×#11715912 |
| Fitting, socle | C3×C5×C7×C37 ⋊ C3 |
| derived, Hall | C7×C37 ⋊ C32×C5 |
| Hall | C5×C7×C37 ⋊ C32 |
| Hall | C5×C37 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C37 ⋊ C3×C5×ΓL(1,𝔽8) |
| Hall | C5×C7 ⋊ C3×C37⋊C3 |
| Sylow | C7 ⋊ C3×C5×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | #11715912 |
| commutator, cosocle, hypocenter | C7×C37 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C37 | C3 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C3×C5 | |
48 conjugacy classes of subgroups.
1335 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×#13095538, C3×C5×#13095536, C3×C5×#13095532, … |
| maximal normal subgroup of | C3×C5×#13095538, C3×C5×#13095536, C3×C5×#13095532, … |
| maximal quotient of | C2×C3×C5×#11715912 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11655, 12);