Finite Group Databasebeta

C2×#20245516 #26370845

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20245516

Splittings

SylowC47 ⋊ C2×#2223

Subgroups

subgroupG/H
centerC22#15689357
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
Fitting, prime radicalC2×C47×#472C2
socleC22×C47#466
hypercenterC2×#472D47
hypocenterC47C2×#2223
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#472

658 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

788 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 324135);