Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C4×C103⋊C16 |
| derived, Sylow | C103 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D103 |
| commutator, hypocenter | C103 | C4×C16 |
| Frattini | C2×C8 | C2×D103 |
| Fitting | C4×C8×C103 | C2 |
| socle | C22×C103 | C2×C8 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C4×C8 | |
58 conjugacy classes of subgroups.
1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×C103⋊C8, C8×C103⋊C16, #27193060, … |
| maximal normal subgroup of | C16×C103⋊C8, C8×C103⋊C16, #27193060, … |
| maximal quotient of | C8×C103⋊C16, #27193062, #27193222, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 323);