Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×#13095519 |
| derived, Sylow | C97 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #87604 |
| commutator, hypocenter | C97 | C23×C8 |
| Frattini | C2 | C23×#87604 |
| Fitting | C22×C4×C97 | C4 |
| socle | C23×C97 | C2×C4 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C22×C4 | |
338 conjugacy classes of subgroups.
448 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20261600, #27157397, #27157403, … |
| maximal normal subgroup of | C2×#20261600, #27157397, #27157403, … |
| maximal quotient of | C22×C4×#11715897, C2×C4×#13095519, C2×#20261703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1620);