Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
| direct product | C2×#15690865 |
| Sylow | C97 ⋊ C2×#97 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×#87604 |
| commutator | C2×C97 | C2×C42 |
| Frattini | C22 | C22×#87604 |
| Fitting | C22×C4×C97 | C4 |
| socle | C23×C97 | C2×C4 |
| hypercenter | C22×C4 | #87604 |
| hypocenter | C97 | C2×#97 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
146 conjugacy classes of subgroups.
424 conjugacy classes — view the full character table.
| maximal subgroup of | #27156575, #27156612, #27156631, … |
| maximal normal subgroup of | #27156575, #27156612, #27156631, … |
| maximal quotient of | C2×#20261577, #27156943, #27156949, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1507);