Finite Group Databasebeta

C16×Dic514 #45666223

order32896
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productC16×Dic514

Splittings

SylowC257 ⋊ Q8×C16

Subgroups

subgroupG/H
centerC2×C16C2×D257
commutatorC2×C257C22×C16
FrattiniC2×C8C22×D257
FittingC4×C16×C257C2
socle, prime radicalC22×C257C22×C8
cosocleC2×C8×C257C23
hypercenterC4×C16D257
hypocenterC257Q8×C16
LCSG ▷ C2×C257 ▷ C257
UCSC1 ◁ C2×C16 ◁ C4×C16

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32896

Conjugacy classes & character table

8272 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32896, 6413);