Finite Group Databasebeta

C2×#20243713 #26217560

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20243713

Splittings

FittingC22×#104×C47 ⋊ C2
SylowC47 ⋊ C2×#1876

Subgroups

subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#104×C47C2
socleC23×C47C4×D4
prime radicalC22×#13094044C2
cosocleC22×C4×C47C24
hypercenterC22×#104D47
hypocenterC47C2×#1876
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#104

1754 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 170850);