Finite Group Databasebeta

C2×#20242136 #26185252

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#20242136

Splittings

SylowC47 ⋊ C2×#1564

Subgroups

subgroupG/H
centerC2×C42D188
commutatorC4×C47C23×C8
FrattiniC42C23×D47
FittingC22×C4×C8×C47C2
socleC23×C47C2×C4⋊C4
prime radicalC24×C47C4⋊C4
cosocleC42×C47C24
hypercenterC22×C4×C8D47
hypocenterC47C2×#1564
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C22×C4×C8

830 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 138542);