Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C193 · Schur multiplier (H2) = C2 |
| direct product | #483×C193 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C193 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C193 |
| prime radical | C23×C193 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C193 ◁ C22×C4×C193 ◁ G | |
104 conjugacy classes of subgroups.
3667 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1608×C193, #1609×C193, #1611×C193, … |
| maximal normal subgroup of | #1608×C193, #1609×C193, #1611×C193, … |
| maximal quotient of | #1823×C193, #1853×C193, #1872×C193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 164);