Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#13110089 |
| Sylow | C103 ⋊ C4×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×D103 |
| commutator | C2×C103 | C2×C42 |
| Frattini | C2×C4 | C22×D103 |
| Fitting | C2×C42×C103 | C2 |
| socle | C22×C103 | C22×C4 |
| hypercenter | C2×C42 | D103 |
| hypocenter | C103 | C4×M16 |
| LCS | G ▷ C2×C103 ▷ C103 | |
| UCS | C1 ◁ C42 ◁ C2×C42 | |
142 conjugacy classes of subgroups.
1672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27192980, #27192981, #27192993, … |
| maximal normal subgroup of | #27192980, #27192981, #27192993, … |
| maximal quotient of | C8×#13110089, #27193433, #27193441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 502);