Finite Group Databasebeta

C2×C4×#88203 #16726979

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×C4×#88203

Splittings

FittingC2×C4×C13×#41 ⋊ C2
SylowC13 ⋊ C2×C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC2×C4×C13×#41C2
socleC23×C13C22×D4
prime radicalC22×#88203C2
cosocleC2×C4×C13C25
hypercenterC2×C4×#41D13
hypocenterC13C2×C4×AGL(1,ℤ/8)
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×#41

3242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033628);