Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C193 · Schur multiplier (H2) = C24 |
| direct product | #539×C193 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C193 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C193 |
| prime radical | #121×C193 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C193 ◁ G | |
218 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
4246 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1597×C193, #1603×C193, #1609×C193, … |
| maximal normal subgroup of | #1597×C193, #1603×C193, #1609×C193, … |
| maximal quotient of | #2313×C193, #2318×C193, #2322×C193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 220);