Finite Group Databasebeta

C2×C4×#88052 #16015550

order3328
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C4×#88052

Splittings

SylowC13 ⋊ C2×C4×M32

Subgroups

subgroupG/H
centerC2×C4×C8C2×D13
commutatorC2×C13C22×C4×C8
FrattiniC2×C8C23×D13
FittingC22×C4×C8×C13C2
socleC23×C13C22×C8
prime radicalC24×C13C2×C8
cosocleC2×C8×C13C24
hypercenterC22×C4×C8D13
hypocenterC13C2×C4×M32
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4×C8 ◁ C22×C4×C8

918 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, 322199);