Finite Group DatabasebetaFinite Group Databasebeta| order | 11470 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C37 · Schur multiplier (H2) = C1 |
| direct product | C5×C37×D31 |
| Fitting, socle, Hall | C5×C31×C37 ⋊ C2 |
| derived, Sylow | C31 ⋊ C2×C5×C37 |
| Hall | C31×C37 ⋊ C2×C5 |
| Hall | C5×C31 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C37 | D31 |
| commutator, cosocle, hypocenter | C31 | C2×C5×C37 |
| Frattini | C1 | G |
| Fitting, socle | C5×C31×C37 | C2 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C5×C37 | |
16 conjugacy classes of subgroups.
3145 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D31×D37, D5×C37×D31, D31×D185, … |
| maximal normal subgroup of | C5×D31×D37, D5×C37×D31, D31×D185, … |
| maximal quotient of | C5×C37×Dic31, C2×C5×C37×D31, C3×C5×C37×D31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11470, 4);