Finite Group Databasebeta

C2×C4×#88060 #15860431

order3328
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×#88060

Splittings

FittingC22×C4×C8×C13 ⋊ C2
SylowC13 ⋊ C2×C4×C22⋊C8

Subgroups

subgroupG/H
centerC22×C42C2×D13
commutatorC2×C13C22×C4×C8
FrattiniC22×C4C23×D13
FittingC22×C4×C8×C13C2
socleC24×C13C22×C4
prime radicalC24×D13C2×C4
cosocleC22×C4×C13C24
hypercenterC22×C4×C8D13
hypocenterC13C2×C4×C22⋊C8
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C42 ◁ C22×C4×C8

2414 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, 167080);