Finite Group Databasebeta

C4×#15689233 #26214760

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#15689233

Splittings

FittingC42×D4×C47 ⋊ C2
SylowC47 ⋊ C4×#442

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D47
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC42×D4×C47C2
socleC23×C47C22×D4
prime radicalC22×#10625334C22
cosocleC22×C4×C47C24
hypercenterC42×D4D47
hypocenterC47C4×#442
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C43 ◁ C42×D4

1326 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, 168050);