Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C47 ⋊ #17308 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D47 |
| commutator, socle, prime radical, cosocle | C24×C47 | C24 |
| Fitting | C47×#1446 | C2 |
| hypercenter | #1446 | D47 |
| hypocenter | C47 | #17308 |
| LCS | G ▷ C24×C47 ▷ C47 | |
| UCS | C1 ◁ C24 ◁ #1446 | |
1034 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1034 conjugacy classes of subgroups — too many to draw. Only its 251 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^8,47|a^2=efg,b^2=efh,c^2=g,d^2=efg,b^a=be,c^a=cf,d^a=dh,i^a=i^46,c^b=cg,d^b=def,i^b=i^46,d^c=de,i^d=i^461058 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 135131);