Finite Group Databasebeta

C2×C4×#88098 #16806719

order3328
isoclinismisoclinic class of #6118
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C4×#88098

Splittings

SylowC13 ⋊ C2×C4×M32

Subgroups

subgroupG/H
centerC2×C42C2×#261
commutatorC2×C13C22×C4×C8
FrattiniC2×C4C23×#261
FittingC2×C4×C8×C13C4
socleC23×C13C22×C8
prime radicalC23×D13C2×C8
cosocleC2×#1055C24
hypercenterC2×C4×C8#261
hypocenterC13C2×C4×M32
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C2×C4×C8

918 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113368);