Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×#15690716 |
| derived, Sylow | C97 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | D97 |
| commutator, hypocenter | C97 | C2×C32 |
| Frattini | C16 | C2×D97 |
| Fitting | C2×C16×C97 | C2 |
| socle | C22×C97 | C16 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C2×C16 | |
34 conjugacy classes of subgroups.
1600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×Dic97, C4×#15690716, #27139869, … |
| maximal normal subgroup of | C32×Dic97, C4×#15690716, #27139869, … |
| maximal quotient of | C4×#15690716, C22⋊#15690716, C4⋊#15690716, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 381);