Finite Group Databasebeta

C2×#20243201 #26213997

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#20243201

Splittings

FittingC2×C4×M16×C47 ⋊ C2
SylowC47 ⋊ C2×#1759

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D47
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC2×C4×M16×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC2×C4×M16D47
hypocenterC47C2×#1759
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×M16

1662 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167287);