Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D824 |
| Fitting | C22×C8×C103 ⋊ C2 |
| Sylow | C103 ⋊ C22×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D412 |
| commutator | C4×C103 | C24 |
| Frattini | C4 | C23×D103 |
| Fitting | C22×C8×C103 | C2 |
| socle | C23×C103 | D4 |
| hypercenter | C22×C8 | D103 |
| hypocenter | C103 | C22×D8 |
| LCS | G ▷ C4×C103 ▷ C2×C103 ▷ C103 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×C8 | |
338 conjugacy classes of subgroups.
1660 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27195491, #27195493, #27196008, … |
| maximal normal subgroup of | #27195491, #27195493, #27196008, … |
| maximal quotient of | C22×#15692943, C22×#15692955, C2×C4×D824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 1319);