Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×C103⋊C16 |
| derived, Sylow | C103 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D103 |
| commutator, hypocenter | C103 | C22×C16 |
| Frattini | C8 | C22×D103 |
| Fitting | C22×C8×C103 | C2 |
| socle | C23×C103 | C8 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C22×C8 | |
98 conjugacy classes of subgroups.
1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27193221, #27193222, #27193233, … |
| maximal normal subgroup of | #27193221, #27193222, #27193233, … |
| maximal quotient of | C2×C4×C103⋊C16, C2×C22⋊(C103⋊C16), C2×C4⋊(C103⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 961);