Finite Group Databasebeta

C2×#20242013 #26184297

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20242013

Splittings

FittingC2×C47×#330 ⋊ C2
SylowC47 ⋊ C2×#1534

Subgroups

subgroupG/H
centerC23C22⋊C4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC2×C47×#330C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC42×C47C24
hypercenterC2×#330D47
hypocenterC47C2×#1534
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

966 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

926 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 137587);