Finite Group Databasebeta

C22×C4×#6094 #16726304

order3328
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×C4×#6094

Splittings

FittingC22×C4×C8×C13 ⋊ C2
SylowC13 ⋊ C22×C4×M16

Subgroups

subgroupG/H
centerC22×C42C2×D13
commutatorC2×C13C23×C42
FrattiniC2×C4C24×D13
FittingC22×C4×C8×C13C2
socleC24×C13C22×C4
prime radicalC24×D13C2×C4
cosocleC2×C4×C13C25
hypercenterC22×C4×C8D13
hypocenterC13C22×C4×M16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C42 ◁ C22×C4×C8

3950 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, 1032953);