Finite Group Databasebeta

C2×C22⋊#88034 #15783110

order3328
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊#88034

Splittings

SylowC13 ⋊ C2×C22⋊C32

Subgroups

subgroupG/H
centerC22×C16C2×D13
commutatorC2×C13C22×C32
FrattiniC2×C16C22×D13
FittingC23×C13×C16C2
socleC23×C13C2×C16
prime radicalC24×C13C16
cosocleC2×C13×C16C23
hypercenterC23×C16D13
hypocenterC13C2×C22⋊C32
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C16 ◁ C23×C16

342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 89759);