Finite Group DatabasebetaFinite Group Databasebeta| order | 6164 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×Dic67 |
| unambiguous semidirect product | C67⋊(C4×C23) |
| derived, Sylow | C67 ⋊ C4×C23 |
| Hall | C23×C67 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D67 |
| commutator, hypocenter | C67 | C4×C23 |
| Frattini | C2 | C23×D67 |
| Fitting, socle | C2×C23×C67 | C2 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C23 | |
12 conjugacy classes of subgroups.
1610 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C23×Dic67, C23×Dic201, C23×(C67⋊C3)⋊C4, … |
| maximal normal subgroup of | C3×C23×Dic67, C23×(C67⋊C3)⋊C4, C5×C23×Dic67 |
| maximal quotient of | C3×C23×Dic67, C23×Dic201, C5×C23×Dic67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6164, 3);