Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×Dic103 |
| Sylow | C103 ⋊ C4×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D103 |
| commutator | C2×C103 | C2×C42 |
| Fitting | C2×M16×C103 | C2 |
| socle | C22×C103 | C22×C4 |
| hypercenter | C2×M16 | D103 |
| hypocenter | C103 | C4×M16 |
| LCS | G ▷ C2×C103 ▷ C103 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M16 | |
142 conjugacy classes of subgroups.
1060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27194935, #100×Dic103, #27194939, … |
| maximal normal subgroup of | #27194935, #100×Dic103, #27194939, … |
| maximal quotient of | M16×C103⋊C8, #27193425, #27193431, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 500);