Finite Group Databasebeta

C2×#20245376 #26370284

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20245376

Splittings

SylowC47 ⋊ C2×#2197

Subgroups

subgroupG/H
centerC22#15689309
commutator, cosocleC2×D4×C47C24
FrattiniC2×D4C23×D47
Fitting, prime radicalC2×C47×B(4,𝔽2)C2
socleC22×C47B(4,𝔽2)
hypercenterC2×B(4,𝔽2)D47
hypocenterC47C2×#2197
LCSG ▷ C2×D4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×B(4,𝔽2)

1320 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

776 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 323574);