Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C103 · Schur multiplier (H2) = C23 |
| direct product | #336×C103 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C103 | C22 |
| commutator | C2 | C4×C8×C103 |
| Frattini, cosocle | C22×C4 | C22×C103 |
| socle, prime radical | C23×C103 | C2×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C103 ◁ G | |
118 conjugacy classes of subgroups.
4120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C103×#1270, C103×#1271, C103×#1272, … |
| maximal normal subgroup of | C103×#1270, C103×#1271, C103×#1272, … |
| maximal quotient of | C103×#1273, C103×#1274, C103×#1275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 17);