Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #106×D97 |
| Fitting | #106×C97 ⋊ C2 |
| Sylow | C97 ⋊ C2×#106 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D97 |
| commutator | C4×C97 | C22×C4 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | #106×C97 | C2 |
| socle | C22×C97 | C2×D4 |
| hypercenter | #106 | D97 |
| hypocenter | C97 | C2×#106 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #106 | |
130 conjugacy classes of subgroups.
700 conjugacy classes — view the full character table.
| maximal subgroup of | #360×D97, #365×D97, C2×#106×D97, … |
| maximal normal subgroup of | #360×D97, #365×D97, C2×#106×D97, … |
| maximal quotient of | #334×D97, #27140490, #27140505, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 578);