Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D4×C103⋊C8 |
| Sylow | C103 ⋊ C8×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D103 |
| commutator | C2×C103 | C22×C8 |
| Fitting | C4×D4×C103 | C2 |
| socle | C22×C103 | C22×C4 |
| hypercenter | C4×D4 | D103 |
| hypocenter | C103 | C8×D4 |
| LCS | G ▷ C2×C103 ▷ C103 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
134 conjugacy classes of subgroups.
1060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27193936, D8×C103⋊C8, SD16×C103⋊C8, … |
| maximal normal subgroup of | #27193936, D8×C103⋊C8, SD16×C103⋊C8, … |
| maximal quotient of | D8×C103⋊C8, SD16×C103⋊C8, Q16×C103⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 615);