Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#13095498 |
| Fitting | C22×Q8×C97 ⋊ C2 |
| Sylow | C97 ⋊ C22×SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22⋊D97 |
| commutator | C4×C97 | C24 |
| Frattini | C4 | C23×D97 |
| Fitting | C22×Q8×C97 | C2 |
| socle | C23×C97 | D4 |
| hypercenter | C22×Q8 | D97 |
| hypocenter | C97 | C22×SD16 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×Q8 | |
298 conjugacy classes of subgroups.
988 conjugacy classes — view the full character table.
| maximal subgroup of | #27142067, #27142073, #27142089, … |
| maximal normal subgroup of | #27142067, #27142073, #27142089, … |
| maximal quotient of | C22×#15690730, C22×#15690734, C22×#15690741, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1321);