Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#15693069 |
| Fitting | C22×Q8×C103 ⋊ C2 |
| Sylow | C103 ⋊ C2×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D103 |
| commutator | C2×C103 | C25 |
| Frattini | C2 | C24×D103 |
| Fitting | C22×Q8×C103 | C2 |
| socle | C22×C103 | C24 |
| hypercenter | C22×Q8 | D103 |
| hypocenter | C103 | C2×2−1+4 |
| LCS | G ▷ C2×C103 ▷ C103 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
794 conjugacy classes of subgroups.
1054 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27195102, #27195105, #27195116, … |
| maximal normal subgroup of | #27195102, #27195105, #27195116, … |
| maximal quotient of | C2×#20268267, C2×#20268269, C2×#20268272, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 1383);