Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #360 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C193 · Schur multiplier (H2) = C2 |
| direct product | #361×C193 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C193 | #102 |
| commutator | C8 | C2×C4×C193 |
| Frattini, cosocle | C2×C8 | C22×C193 |
| prime radical | C2×D8×C193 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C193 ◁ C2×C4×C193 ◁ C2×C8×C193 ◁ G | |
62 conjugacy classes of subgroups.
3088 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#361×C193, #2148×C193, AGL(1,ℤ/16)×C193, … |
| maximal normal subgroup of | C2×#361×C193, #2148×C193, AGL(1,ℤ/16)×C193, … |
| maximal quotient of | #1333×C193, #1349×C193, #1361×C193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 42);