Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16×C47 · Schur multiplier (H2) = C22 |
| direct product | C47×#13630 |
| subgroup | G/H | |
|---|---|---|
| center | C16×C47 | C2×D4 |
| commutator | C4 | C22×C16×C47 |
| Frattini, cosocle | C2×C16 | C23×C47 |
| socle | C2×C47 | C2×C4⋊C16 |
| prime radical | C23×C47 | M32 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C47 ◁ C22×C16×C47 ◁ G | |
198 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
4136 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 6618);