Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3055 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C23×C4 |
| direct product | C61×#3139 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C61 |
| prime radical | C23×C61 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G | |
380 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1952 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 1871);