Finite Group Databasebeta

C2×#20242045 #26184576

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20242045

Splittings

SylowC47 ⋊ C2×#1542

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC2×C47×#533C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22⋊C4
cosocleC42×C47C24
hypercenterC2×#533D47
hypocenterC47C2×#1542
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#533

1050 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, 137866);