Finite Group Databasebeta

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C2×#20244677 #26244142

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

Aliases

direct productC2×#20244677

Splittings

SylowC47 ⋊ C2×#2051

Subgroups

subgroupG/H
centerC23#13093996
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
Fitting, prime radicalC22×AGL(1,ℤ/8)×C47C2
socleC23×C47#121
hypercenterC22×AGL(1,ℤ/8)D47
hypocenterC47C2×#2051
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

1490 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 197432);