Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C103 · Schur multiplier (H2) = C1 |
| direct product | Q64×C103 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C2×C103 | D16 |
| commutator, Frattini, cosocle | C16 | C22×C103 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C103 ◁ C4×C103 ◁ C8×C103 ◁ C16×C103 ◁ G | |
30 conjugacy classes of subgroups.
1957 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C103×SD128, C103×Q128, C2×Q64×C103, … |
| maximal normal subgroup of | C103×SD128, C103×Q128, C2×Q64×C103, … |
| maximal quotient of | C103×#1416, C103×#1423, C2×Q64×C103 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 54);