Finite Group Databasebeta

C4×#15689096 #26213930

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

Aliases

direct productC4×#15689096

Splittings

FittingC4×#117×C47 ⋊ C2
SylowC47 ⋊ C4×#410

Subgroups

subgroupG/H
centerC42(C2×D47)⋊C4
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC4×#117×C47C2
socleC22×C47C22×C22⋊C4
prime radicalC22×#10625350C22
cosocleC24×C47C24
hypercenterC4×#117D47
hypocenterC47C4×#410
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C42 ◁ C22×C42 ◁ C4×#117

1666 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, 167220);