Finite Group Databasebeta

C42×#6105 #15861389

order3328
isoclinismisoclinic class of #6104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC42×#6105

Splittings

SylowC13 ⋊ C42×SD16

Subgroups

subgroupG/H
centerC2×C42C22⋊D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC42×D4×C13C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenterC42×D4D13
hypocenterC13C42×SD16
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×D4

1230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 168038);