Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| isoclinism | isoclinic class of D97 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×C4×D97 |
| Fitting | C23×C4×C97 ⋊ C2 |
| derived, Sylow | C97 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D97 |
| commutator, hypocenter | C97 | C24×C4 |
| Frattini | C2 | C24×D97 |
| Fitting | C23×C4×C97 | C2 |
| socle | C24×C97 | C22 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C23×C4 | |
1362 conjugacy classes of subgroups.
1600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27139957, #27141645, C2×#95×D97, … |
| maximal normal subgroup of | #27139957, #27141645, C2×#95×D97, … |
| maximal quotient of | C22×C42×D97, C23×C4×Dic97, C22×C22⋊C4×D97, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1367);