Finite Group Databasebeta

C2×#20242309 #26188352

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20242309

Splittings

FittingC2×C47×#450 ⋊ C2
SylowC47 ⋊ C2×#1596

Subgroups

subgroupG/H
centerC23#13093992
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#450C2
socleC23×C47#120
prime radicalC2×#15689031C2
hypercenterC2×#450D47
hypocenterC47C2×#1596
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

1696 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

920 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 141642);