Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C103 · Schur multiplier (H2) = C22 |
| direct product | #504×C103 |
| subgroup | G/H | |
|---|---|---|
| center | C16×C103 | C22 |
| commutator | C2 | C22×C8×C103 |
| Frattini, cosocle | C8 | C23×C103 |
| socle | C2×C103 | C22×C8 |
| prime radical | #41×C103 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C103 ◁ G | |
84 conjugacy classes of subgroups.
4120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C103×#1401, C103×#2170, C103×#2171, … |
| maximal normal subgroup of | C103×#1401, C103×#2170, C103×#2171, … |
| maximal quotient of | C103×#2108, C103×#2113, C103×#2151, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 185);