Finite Group Databasebeta

C4×#15689243 #26214850

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#15689243

Splittings

FittingC4×#131×C47 ⋊ C2
SylowC47 ⋊ C4×#444

Subgroups

subgroupG/H
centerC42C2×C22⋊D47
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC4×#131×C47C2
socleC22×C47C2×C4×D4
prime radicalC2×#13094044C22
cosocleC22×C4×C47C24
hypercenterC4×#131D47
hypocenterC47C4×#444
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C42 ◁ C2×C4×C8 ◁ C4×#131

1022 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 168140);