Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C103 · Schur multiplier (H2) = C25 |
| direct product | C2×#131×C103 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C103 | C22 |
| commutator | C2 | C23×C4×C103 |
| Frattini, cosocle | C4 | C24×C103 |
| socle | C22×C103 | C22×C4 |
| prime radical | C2×#41×C103 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C103 ◁ G | |
266 conjugacy classes of subgroups.
4120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C103×#1757, C103×#1764, C103×#1765, … |
| maximal normal subgroup of | C103×#1757, C103×#1764, C103×#1765, … |
| maximal quotient of | C2×#405×C103, C4×#131×C103, C2×#408×C103, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 248);