Finite Group Databasebeta

C2×#20247379 #26383801

order12032
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#20247379

Splittings

FittingC22×C4×D4×C47 ⋊ C2
SylowC47 ⋊ C2×#2463

Subgroups

subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC22×C4×D4×C47C2
socleC24×C47C24
prime radicalC2×#15689031C2
hypercenterC22×C4×D4D47
hypocenterC47C2×#2463
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C4×D4

3958 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 337091);