Finite Group Databasebeta

C2×C4×C16×D13 #16015540

order3328
isoclinismisoclinic class of D13
automorphism?
homologyAbelianization (H1) = C22×C4×C16 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C16×D13

Splittings

FittingC2×C4×C13×C16 ⋊ C2
derived, SylowC13 ⋊ C22×C4×C16

Subgroups

subgroupG/H
center, hypercenterC2×C4×C16D13
commutator, hypocenterC13C22×C4×C16
FrattiniC2×C8C23×D13
FittingC2×C4×C13×C16C2
socleC23×C13C22×C8
prime radicalC23×D13C2×C8
cosocleC2×C8×C13C24
LCSG ▷ C13
UCSC1 ◁ C2×C4×C16

1022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

1024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322189);