Finite Group Databasebeta

C2×#20241508 #26131232

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#20241508

Splittings

SylowC47 ⋊ C2×#1391

Subgroups

subgroupG/H
centerC2×C4#13093938
commutatorC23×C47C2×C42
FrattiniC2×#41C22×D47
FittingC2×C47×#410C2
socleC22×C47#342
prime radicalC22×#41×C47C22
cosocleC2×#41×C47C23
hypercenterC2×#410D47
hypocenterC47C2×#1391
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

782 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84522);