Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C2×#15690905 |
| derived, Sylow | C97 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11715906 |
| commutator, hypocenter | C97 | C22×C16 |
| Frattini | C2 | C22×#11715906 |
| Fitting | C2×C4×C97 | C8 |
| socle | C22×C97 | C2×C8 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C2×C4 | |
98 conjugacy classes of subgroups.
160 conjugacy classes — view the full character table.
| maximal subgroup of | #27158807, #27158816, #27158817, … |
| maximal normal subgroup of | #27158807, #27158816, #27158817, … |
| maximal quotient of | C2×C4×#13095523, C4×#15690905, #27158901, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1666);