Finite Group Databasebeta

C2×#20241457 #26127845

order12032
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20241457

Splittings

SylowC47 ⋊ C2×#1370

Subgroups

subgroupG/H
centerC22×C8C22⋊D47
commutatorC4×C47C22×C16
FrattiniC4×C8C22×D47
FittingC2×C47×C4⋊C16C2
socle, prime radicalC23×C47C4⋊C8
cosocleC4×C8×C47C23
hypercenterC2×C4⋊C16D47
hypocenterC47C2×#1370
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C4⋊C16

286 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 81135);