Finite Group Databasebeta

C2×#20245601 #26371161

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

Aliases

direct productC2×#20245601

Splittings

FittingC2×C47×#361 ⋊ C2
SylowC47 ⋊ C2×#2238

Subgroups

subgroupG/H
centerC22#15689440
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC2×C47×#361C2
socleC22×C47#481
prime radicalC2×#15689373C2
hypercenterC2×#361D47
hypocenterC47C2×#2238
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

604 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

776 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 324451);