Finite Group Databasebeta

← Prev (#26213738) Next (#26213740) →

C2×#20243133 #26213739

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C42

Aliases

direct productC2×#20243133

Splittings

SylowC47 ⋊ C2×#1744

Subgroups

subgroupG/H
centerC22×C42C2×D47
commutatorC2×C47C22×C4×C8
FrattiniC22×C4C23×D47
FittingC22×C4×C8×C47C2
socle, prime radicalC24×C47C22×C4
cosocleC22×C4×C47C24
hypercenterC22×C4×C8D47
hypocenterC47C2×#1744
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C42 ◁ C22×C4×C8

1438 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167029);