Finite Group Databasebeta

C2×#13113118 #15828496

order3328
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C8

Aliases

direct productC2×#13113118

Splittings

FittingC2×C82×C13 ⋊ C2
SylowC13 ⋊ C2×#1450

Subgroups

subgroupG/H
centerC2×C4×C8C2×D13
commutatorC2×C13C22×C4×C8
FrattiniC42C23×D13
FittingC2×C82×C13C2
socleC23×C13C2×C42
prime radicalC23×D13C42
cosocleC42×C13C24
hypercenterC2×C82D13
hypocenterC13C2×#1450
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4×C8 ◁ C2×C82

982 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, 135145);