Finite Group Databasebeta

C4×#15688882 #26121450

order12032
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct productC4×#15688882

Splittings

SylowC47 ⋊ C4×#339

Subgroups

subgroupG/H
centerC2×C42C22⋊D47
commutatorC4×C47C43
FrattiniC23×C4C22×D47
FittingC4×#117×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenterC4×#117D47
hypocenterC47C4×#339
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C4×#117

1214 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 74740);