Finite Group Databasebeta

C2×#20241985 #26184179

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#20241985

Splittings

FittingC2×C4×M16×C47 ⋊ C2
SylowC47 ⋊ C2×#1527

Subgroups

subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC2×C4×M16×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D188C4
cosocleC42×C47C24
hypercenterC2×C4×M16D47
hypocenterC47C2×#1527
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×M16

1394 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, 137469);