Finite Group Databasebeta

C2×#22549633 #30638431

order16256
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#22549633

Splittings

SylowC127 ⋊ C2×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC2×C4C4×Dic127
commutatorC4×C127C2×C42
FrattiniC22×C4C22×D127
FittingC22×M16×C127C2
socleC22×C127#95
prime radicalC24×C127D4
cosocleC22×C4×C127C23
hypercenterC22×M16D127
hypocenterC127C2×H(3,ℤ/4)
LCSG ▷ C4×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C22×M16

404 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 4211);