Finite Group Databasebeta

C2×#20244682 #26244147

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

Aliases

direct productC2×#20244682

Splittings

FittingC22×#108×C47 ⋊ C2
SylowC47 ⋊ C2×#2051

Subgroups

subgroupG/H
centerC23#13093999
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC22×#108×C47C2
socleC23×C47#121
prime radicalC22×#13094052C2
hypercenterC22×#108D47
hypocenterC47C2×#2051
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#108

1490 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 197437);