Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12715 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C47 · Schur multiplier (H2) = C25 |
| direct product | C47×#12718 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C47 | #1781 |
| commutator | C22×C4 | C22×C4×C47 |
| Frattini, cosocle | C2×#41 | C23×C47 |
| prime radical | C47×#3498 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C47 ◁ C2×C4×C47 ◁ C2×H(5,𝔽2)×C47 ◁ G | |
1080 conjugacy classes of subgroups.
1598 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 5706);