Finite Group Databasebeta

C4×#15688913 #26131415

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

Aliases

direct productC4×#15688913

Splittings

SylowC47 ⋊ C4×#352

Subgroups

subgroupG/H
centerC2×C4#13093939
commutatorC23×C47C2×C42
FrattiniC22×D4C22×D47
FittingC4×#123×C47C2
socleC22×C47C2×#99
prime radical, cosocleC22×D4×C47C23
hypercenterC4×#123D47
hypocenterC47C4×#352
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#123

576 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84705);