Finite Group Databasebeta

C4×#15689097 #26213929

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

Aliases

direct productC4×#15689097

Splittings

SylowC47 ⋊ C4×#410

Subgroups

subgroupG/H
centerC42C22⋊Dic47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC2×C4×#41×C47C2
socleC22×C47C22×C22⋊C4
prime radicalC22×#41×C47C22
cosocleC24×C47C24
hypercenterC2×C4×#41D47
hypocenterC47C4×#410
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C42 ◁ C22×C42 ◁ C2×C4×#41

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, 167219);