Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C97 · Schur multiplier (H2) = C23 |
| direct product | C2×#104×C97 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C97 | D4 |
| commutator | C4 | C22×C4×C97 |
| Frattini, cosocle | C2×C4 | C23×C97 |
| socle | C22×C97 | C22⋊C4 |
| prime radical | C2×#41×C97 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C97 ◁ C22×C4×C97 ◁ G | |
170 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2716 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#104×C97, C97×#1759, C97×#1764, … |
| maximal normal subgroup of | C4×#104×C97, C97×#1759, C97×#1764, … |
| maximal quotient of | C2×D4⋊C8×C97, C2×Q8⋊C8×C97, C97×#1476, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 101);