Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×C4×Dic206 |
| Sylow | C103 ⋊ C2×C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D103 |
| commutator | C2×C103 | C23×C4 |
| Frattini | C22 | C23×D103 |
| Fitting | C2×C42×C103 | C2 |
| socle | C23×C103 | C23 |
| hypercenter | C2×C42 | D103 |
| hypocenter | C103 | C2×C4×Q8 |
| LCS | G ▷ C2×C103 ▷ C103 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
298 conjugacy classes of subgroups.
1672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27193467, #27193487, C2×#20267521, … |
| maximal normal subgroup of | #27193467, #27193487, C2×#20267521, … |
| maximal quotient of | C2×C4×C4⋊Dic103, C2×C4×Dic103⋊C4, C42×Dic206, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 1014);