Finite Group Databasebeta

C2×Dic416 #15783969

order3328
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic416

Splittings

SylowC13 ⋊ C2×Q128

Subgroups

subgroupG/H
centerC22D416
commutator, cosocleC13×C32C23
FrattiniC32C22×D13
FittingC2×C13×C64C2
socle, prime radicalC22×C13D32
hypercenterC2×C64D13
hypocenterC13C2×Q128
LCSG ▷ C13×C32 ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ C2×C64

126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 90618);