Finite Group Databasebeta

C2×#13113650 #15832306

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13113650

Splittings

FittingC2×C13×#322 ⋊ C2
SylowC13 ⋊ C2×SD16⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D52
commutatorC4×C13C23×C8
FrattiniC42C23×D13
FittingC2×C13×#322C2
socleC23×C13C4×D4
prime radicalC22×D52C2×C4
cosocleC42×C13C24
hypercenterC2×#322D13
hypocenterC13C2×SD16⋊C8
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#322

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 138955);