Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C97 · Schur multiplier (H2) = C23 |
| direct product | #417×C97 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C97 | C2×D4 |
| commutator | C4 | C22×C4×C97 |
| Frattini, cosocle | C2×C4 | C23×C97 |
| prime radical | C2×#41×C97 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C97 ◁ C22×C4×C97 ◁ G | |
162 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 162 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.
2134 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C97×#1792, C97×#1793, C97×#1815, … |
| maximal normal subgroup of | C97×#1792, C97×#1793, C97×#1815, … |
| maximal quotient of | C97×#1477, C97×#1483, C97×#1489, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 98);