Finite Group Databasebeta

C2×C4×#88056 #15860664

order3328
isoclinismisoclinic class of #6095
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×#88056

Splittings

SylowC13 ⋊ C2×C4×#103

Subgroups

subgroupG/H
centerC23×C4D52
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC22×C4×C8×C13C2
socle, prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenterC22×C4×C8D13
hypocenterC13C2×C4×#103
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×C8

1726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 167313);