Finite Group Databasebeta

C2×#20245341 #26370170

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

Aliases

direct productC2×#20245341

Splittings

FittingC2×C47×#349 ⋊ C2
SylowC47 ⋊ C2×#2191

Subgroups

subgroupG/H
centerC22#15689259
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC2×C47×#349C2
socleC22×C47#447
prime radicalC2×#15689923C2
hypercenterC2×#349D47
hypocenterC47C2×#2191
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#349

1128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1052 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 323460);