Finite Group Databasebeta

C2×#354×D47 #26369051

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#354×D47

Splittings

FittingC2×C47×#354 ⋊ C2
SylowC47 ⋊ C22×#354

Subgroups

subgroupG/H
centerC22#99×D47
commutatorC2×C4×C47C23×C4
FrattiniC2×D4C23×D47
FittingC2×C47×#354C2
socleC22×C47C2×#99
prime radicalC22×D4×D47C22
cosocleC2×D4×C47C24
hypercenterC2×#354D47
hypocenterC47C22×#354
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#354

1502 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

650 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322341);