Finite Group Databasebeta

C2×Dic2032 #30641035

order16256
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic2032

Splittings

SylowC127 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC22D2032
commutator, cosocleC16×C127C23
FrattiniC16C22×D127
FittingC2×C32×C127C2
socle, prime radicalC22×C127D16
hypercenterC2×C32D127
hypocenterC127C2×Q64
LCSG ▷ C16×C127 ▷ C8×C127 ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 6815);