Finite Group Databasebeta

C2×#20241728 #26182138

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20241728

Splittings

FittingC2×C47×#432 ⋊ C2
SylowC47 ⋊ C2×#1466

Subgroups

subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#432C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D188C4
cosocleC22×C4×C47C24
hypercenterC2×#432D47
hypocenterC47C2×#1466
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

1650 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 135428);