Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 188416 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C8 |
| abelian | C8×C32×C47 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4×C16 | C22×C47 |
| socle, prime radical | C22×C47 | C4×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
134 conjugacy classes of subgroups.
12032 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×C47×C64, C16×C32×C47, C2×C8×C32×C47 |
| maximal normal subgroup of | C8×C47×C64, C16×C32×C47, C2×C8×C32×C47 |
| maximal quotient of | C8×C47×C64, C16×C32×C47, C2×C8×C32×C47 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 316);