Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
No aliases for this group.
| Fitting | C47×#2868 ⋊ C2 |
| Sylow | C47 ⋊ #36644 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D47 |
| commutator, socle, cosocle | C23×C47 | C25 |
| Fitting | C47×#2868 | C2 |
| hypercenter | #2868 | D47 |
| hypocenter | C47 | #36644 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #2868 | |
4086 conjugacy classes of subgroups; only the 811 normal subgroups are shown.
This group has 4086 conjugacy classes of subgroups — too many to draw. Only its 811 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^8,47|c^2=g,d^2=h,e^2=f,b^a=bf,c^a=cg,d^a=dh,i^a=i^46,i^b=i^46,i^e=i^461100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 375673);