Finite Group Databasebeta

C4×#15688932 #26131529

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#15688932

Splittings

FittingC4×#106×C47 ⋊ C2
SylowC47 ⋊ C4×#360

Subgroups

subgroupG/H
centerC2×C4#13093944
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC4×#106×C47C2
socleC22×C47C2×#102
prime radicalC2×#13094046C22
cosocleC22×C8×C47C23
hypercenterC4×#106D47
hypocenterC47C4×#360
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#106

466 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84819);