Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C103 · Schur multiplier (H2) = C22 |
| direct product | #338×C103 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C103 | C42 |
| commutator | C4 | C42×C103 |
| Frattini, cosocle | C22×C4 | C22×C103 |
| socle | C2×C103 | #95 |
| prime radical | C23×C103 | Q8 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C4×C103 ◁ G | |
86 conjugacy classes of subgroups.
2266 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C103×#1341, C103×#1342, C2×#338×C103, … |
| maximal normal subgroup of | C103×#1341, C103×#1342, C2×#338×C103, … |
| maximal quotient of | C103×#1275, C103×#1291, C103×#1292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 19);