Finite Group Databasebeta

C4×#15689561 #26369600

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#15689561

Splittings

FittingC4×M32×C47 ⋊ C2
SylowC47 ⋊ C4×#509

Subgroups

subgroupG/H
centerC2×C4C2×D376
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC4×M32×C47C2
socleC22×C47C22×D8
prime radicalC2×#15689561C2
cosocleC2×C8×C47C24
hypercenterC4×M32D47
hypocenterC47C4×#509
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×M32

738 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322890);