Finite Group Databasebeta

C2×#20243268 #26214285

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

Aliases

direct productC2×#20243268

Splittings

SylowC47 ⋊ C2×#1772

Subgroups

subgroupG/H
centerC22×C8C22⋊D47
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC2×C47×#405C2
socleC23×C47C4×D4
prime radicalC24×C47#41
cosocleC22×C4×C47C24
hypercenterC2×#405D47
hypocenterC47C2×#1772
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C2×#405

1102 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167575);