Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#13095519 |
| derived, Sylow | C97 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #87604 |
| commutator, hypocenter | C97 | C2×C4×C8 |
| Frattini | C22 | C22×#87604 |
| Fitting | C42×C97 | C4 |
| socle | C22×C97 | C22×C4 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C42 | |
162 conjugacy classes of subgroups.
448 conjugacy classes — view the full character table.
| maximal subgroup of | #27156565, #27156567, #27156570, … |
| maximal normal subgroup of | #27156565, #27156567, #27156570, … |
| maximal quotient of | C8×#13095519, #27156930, #27156934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1505);