Finite Group Databasebeta

C2×C4×#88065 #15860632

order3328
isoclinismisoclinic class of #6104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×#88065

Splittings

FittingC2×C4×C13×M16 ⋊ C2
SylowC13 ⋊ C2×C4×#104

Subgroups

subgroupG/H
centerC2×C42C22⋊D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC2×C4×C13×M16C2
socleC23×C13C2×C22⋊C4
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenterC2×C4×M16D13
hypocenterC13C2×C4×#104
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C2×C4×M16

1878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 167281);