Finite Group Databasebeta

C2×#20241572 #26136729

order12032
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20241572

Splittings

SylowC47 ⋊ C2×#1417

Subgroups

subgroupG/H
centerC2×C4#13093965
commutatorC16×C47C22×C4
FrattiniC2×C16C22×D47
Fitting, prime radicalC2×C47×#508C2
socleC22×C47#357
cosocleC2×C16×C47C23
hypercenterC2×#508D47
hypocenterC47C2×#1417
LCSG ▷ C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C2×#508

294 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 90019);