Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2021 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C47 · Schur multiplier (H2) = C25 |
| direct product | C47×#8317 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C47 | #120 |
| commutator | C24 | C22×C4×C47 |
| Frattini, cosocle | C23×C4 | C23×C47 |
| socle | C22×C47 | #379 |
| prime radical | C47×#3459 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C47 ◁ C23×C4×C47 ◁ G | |
864 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1305);