Finite Group DatabasebetaFinite Group Databasebeta| order | 7612 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic173 |
| derived, Sylow | C173 ⋊ C4×C11 |
| Hall | C11×C173 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D173 |
| commutator, hypocenter | C173 | C4×C11 |
| Frattini | C2 | C11×D173 |
| Fitting, socle | C2×C11×C173 | C2 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C2×C11 | |
12 conjugacy classes of subgroups.
1936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×Dic173, C11×Dic519, C5×C11×Dic173, … |
| maximal normal subgroup of | C3×C11×Dic173, C5×C11×Dic173, C11⋊C5×Dic173 |
| maximal quotient of | C3×C11×Dic173, C11×Dic519, C5×C11×Dic173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7612, 3);