Finite Group Databasebeta

C22×Dic208 #16021042

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic208

Splittings

SylowC13 ⋊ C22×Q64

Subgroups

subgroupG/H
centerC23D208
commutator, cosocleC13×C16C24
FrattiniC16C23×D13
FittingC22×C13×C32C2
socle, prime radicalC23×C13D16
hypercenterC22×C32D13
hypocenterC13C22×Q64
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C22×C32

462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 327691);