Finite Group Databasebeta

C2×#20244424 #26243178

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20244424

Splittings

FittingC22×C4⋊Q8×C47 ⋊ C2
SylowC47 ⋊ C2×#2005

Subgroups

subgroupG/H
centerC23#13093992
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC22×C4⋊Q8×C47C2
socleC23×C47#120
prime radicalC22×#10625350C22
hypercenterC22×C4⋊Q8D47
hypocenterC47C2×#2005
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊Q8

1998 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, 196468);