Finite Group Databasebeta

C4×#11719450 #16726332

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

Aliases

direct productC4×#11719450

Splittings

FittingC2×C4×C13×M16 ⋊ C2
SylowC13 ⋊ C4×#568

Subgroups

subgroupG/H
centerC42C23×D13
commutatorC2×C13C23×C42
FrattiniC2×C4C24×D13
FittingC2×C4×C13×M16C2
socleC22×C13C24×C4
prime radicalC22×#6127C22
cosocleC2×C4×C13C25
hypercenterC2×C4×M16D13
hypocenterC13C4×#568
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C42 ◁ C2×C4×M16

3250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1032981);