Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C103 · Schur multiplier (H2) = C22 |
| direct product | #331×C103 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C103 | C22⋊C4 |
| commutator | C2×C4 | C2×C4×C103 |
| Frattini, cosocle | C42 | C22×C103 |
| prime radical | #127×C103 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C42×C103 ◁ G | |
84 conjugacy classes of subgroups.
1957 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C103×#1402, C2×#331×C103, C103×#1540, … |
| maximal normal subgroup of | C103×#1402, C2×#331×C103, C103×#1540, … |
| maximal quotient of | C103×#1270, C103×#1296, C103×#1357, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 12);