Finite Group Databasebeta

C4×#15689541 #26368924

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#15689541

Splittings

FittingC4×M32×C47 ⋊ C2
SylowC47 ⋊ C4×#504

Subgroups

subgroupG/H
centerC4×C8C22×D47
commutatorC2×C47C22×C4×C8
FrattiniC2×C8C23×D47
FittingC4×M32×C47C2
socleC22×C47C23×C8
prime radicalC2×#10625350C2×C4
cosocleC2×C8×C47C24
hypercenterC4×M32D47
hypocenterC47C4×#504
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C4×C8 ◁ C4×M32

834 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322214);