Finite Group Databasebeta

C2×#20241373 #26126419

order12032
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#20241373

Splittings

SylowC47 ⋊ C2×#1339

Subgroups

subgroupG/H
centerC22#15688857
commutatorC2×C8×C47C22×C4
FrattiniC2×M16C22×D47
Fitting, prime radicalC2×C47×#469C2
socleC22×C47#327
cosocleC2×M16×C47C23
hypercenterC2×#469D47
hypocenterC47C2×#1339
LCSG ▷ C2×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#469

496 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, 79709);