Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7394 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C47 · Schur multiplier (H2) = C23 |
| direct product | C47×#7394 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C47 | #1343 |
| commutator | C2×C22⋊C4 | C2×C4×C47 |
| Frattini, cosocle | #379 | C22×C47 |
| prime radical | C47×#2021 | C2 |
| LCS | G ▷ C2×C22⋊C4 ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C47 ◁ C23×C47 ◁ C24×C47 ◁ C47×#379 ◁ G | |
418 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1175 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 382);