Finite Group DatabasebetaFinite Group Databasebeta| order | 11655 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#14556419 |
| derived, Hall | C7×C37 ⋊ C5×C9 |
| Hall | C5×C7×C37 ⋊ C9 |
| Hall | C5×C37 ⋊ C7⋊C9 |
| Sylow | C37 ⋊ C5×C7⋊C9 |
| Hall | C5×C7 ⋊ #66524 |
| Sylow | C7 ⋊ C5×#66524 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | #11715913 |
| commutator, hypocenter | C7×C37 | C5×C9 |
| Frattini | C3 | C5×#11715913 |
| Fitting, socle, prime radical | C3×C5×C7×C37 | C3 |
| cosocle | C3×C7×C37 | C3×C5 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C3×C5 | |
24 conjugacy classes of subgroups.
1335 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×#14556419, C5×#17987931, C5×#17987935, … |
| maximal normal subgroup of | C2×C5×#14556419, C5×#17987931, C5×#17987935, … |
| maximal quotient of | C2×C5×#14556419 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11655, 4);