Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×C103⋊C8 |
| unambiguous semidirect product | C103⋊C82 |
| derived, Sylow | C103 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D103 |
| commutator, hypocenter | C103 | C82 |
| Frattini | C42 | C2×D103 |
| Fitting | C4×C8×C103 | C2 |
| socle | C22×C103 | C42 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C4×C8 | |
74 conjugacy classes of subgroups.
1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×C103⋊C8, #27193060, #27193063, … |
| maximal normal subgroup of | C16×C103⋊C8, #27193060, #27193063, … |
| maximal quotient of | C103⋊#1273, C16×C103⋊C8, C8×C103⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 269);