Finite Group Databasebeta

C2×#20241347 #26125994

order12032
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20241347

Splittings

FittingC2×C47×#346 ⋊ C2
SylowC47 ⋊ C2×#1330

Subgroups

subgroupG/H
centerC22×C4(C2×D47)⋊C4
commutatorC2×C4×C47C22×C8
FrattiniC4×C8C22×D47
FittingC2×C47×#346C2
socleC23×C47C22⋊C8
prime radicalC22×D188C8
cosocleC4×C8×C47C23
hypercenterC2×#346D47
hypocenterC47C2×#1330
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#346

422 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 79284);