Finite Group Databasebeta

C2×C4×#88202 #16726323

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C4×#88202

Splittings

SylowC13 ⋊ C2×C4×#131

Subgroups

subgroupG/H
centerC2×C42C22×D13
commutatorC2×C13C23×C42
FrattiniC2×C4C24×D13
FittingC2×C4×C13×#41C2
socleC23×C13C23×C4
prime radicalC22×C13×#41C22
cosocleC2×C4×C13C25
hypercenterC2×C4×#41D13
hypocenterC13C2×C4×#131
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C2×C4×#41

3366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1032972);