Finite Group DatabasebetaFinite Group Databasebeta| order | 7124 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic137 |
| derived, Sylow | C137 ⋊ C4×C13 |
| Hall | C13×C137 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D137 |
| commutator, hypocenter | C137 | C4×C13 |
| Frattini | C2 | C13×D137 |
| Fitting, socle | C2×C13×C137 | C2 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C2×C13 | |
12 conjugacy classes of subgroups.
1820 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C13×Dic137, C13×Dic411, C13⋊C3×Dic137, … |
| maximal normal subgroup of | C3×C13×Dic137, C13⋊C3×Dic137, C5×C13×Dic137 |
| maximal quotient of | C3×C13×Dic137, C13×Dic411, C5×C13×Dic137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7124, 3);