Finite Group Databasebeta

C4×#15689095 #26213927

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

Aliases

direct productC4×#15689095

Splittings

FittingC4×#99×C47 ⋊ C2
SylowC47 ⋊ C4×#410

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC4×#99×C47C2
socleC22×C47C22×C22⋊C4
prime radicalC22×#10625352C22
cosocleC24×C47C24
hypercenterC4×#99D47
hypocenterC47C4×#410
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

1666 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167217);