Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C103 · Schur multiplier (H2) = C22 |
| direct product | #435×C103 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C103 | C23 |
| commutator | C22 | C22×C4×C103 |
| Frattini, cosocle | C2×C4 | C23×C103 |
| socle | C22×C103 | C22×C4 |
| prime radical | C2×D4×C103 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C103 ◁ G | |
124 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2884 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#435×C103, C103×#2929, C103×#2930, … |
| maximal normal subgroup of | C2×#435×C103, C103×#2929, C103×#2930, … |
| maximal quotient of | C103×#1581, C103×#1582, C103×#1583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 116);