Finite Group Databasebeta

← Prev (#26213789) Next (#26213791) →

C2×C4×(C2×D47)⋊C8 #26213790

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×(C2×D47)⋊C8

Splittings

FittingC22×C4×C8×C47 ⋊ C2
SylowC47 ⋊ C2×C4×C22⋊C8

Subgroups

subgroupG/H
centerC22×C42C2×D47
commutatorC2×C47C22×C4×C8
FrattiniC22×C4C23×D47
FittingC22×C4×C8×C47C2
socleC24×C47C22×C4
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenterC22×C4×C8D47
hypocenterC47C2×C4×C22⋊C8
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C42 ◁ C22×C4×C8

2414 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, 167080);