Finite Group Databasebeta

C4×#15689120 #26214030

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

Aliases

direct productC4×#15689120

Splittings

FittingC22×C4×C8×C47 ⋊ C2
SylowC47 ⋊ C4×#416

Subgroups

subgroupG/H
centerC2×C42D188
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC22×C4×C8×C47C2
socleC23×C47C22×D4
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC22×C4×C8D47
hypocenterC47C4×#416
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C22×C4×C8

1670 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167320);