Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#13110106 |
| Fitting | C22×Q8×C103 ⋊ C2 |
| Sylow | C103 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D103 |
| commutator | C2×C103 | C25 |
| Frattini | C2 | C24×D103 |
| Fitting | C22×Q8×C103 | C2 |
| socle | C23×C103 | C23 |
| hypercenter | C22×Q8 | D103 |
| hypocenter | C103 | C22×#41 |
| LCS | G ▷ C2×C103 ▷ C103 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
890 conjugacy classes of subgroups.
1060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27195071, #27195083, #27197633, … |
| maximal normal subgroup of | #27195071, #27195083, #27197633, … |
| maximal quotient of | C22×#15692979, C22×#15692983, C22×Q8×Dic103, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 1377);