Finite Group Databasebeta

C2×#20241344 #26125978

order12032
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20241344

Splittings

FittingC2×C4×C16×C47 ⋊ C2
SylowC47 ⋊ C2×D4⋊C16

Subgroups

subgroupG/H
centerC22×C8D188
commutatorC4×C47C22×C16
FrattiniC4×C8C22×D47
FittingC2×C4×C16×C47C2
socleC23×C47C22⋊C8
prime radicalC22×D188C8
cosocleC4×C8×C47C23
hypercenterC2×C4×C16D47
hypocenterC47C2×D4⋊C16
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C4×C16

470 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 79268);