Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C193 · Schur multiplier (H2) = C22 |
| direct product | #444×C193 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C193 | C2×D4 |
| commutator | C4 | C22×C4×C193 |
| Frattini, cosocle | C2×C4 | C23×C193 |
| socle | C2×C193 | C4×D4 |
| prime radical | #135×C193 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C193 ◁ C2×C8×C193 ◁ G | |
104 conjugacy classes of subgroups.
4246 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2180×C193, AGL(1,ℤ/16)×C193 |
| maximal normal subgroup of | #2180×C193, AGL(1,ℤ/16)×C193 |
| maximal quotient of | SD16⋊C8×C193, #1579×C193, #1580×C193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 125);