Finite Group Databasebeta

C2×#13113452 #15830850

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13113452

Splittings

SylowC13 ⋊ C2×#1531

Subgroups

subgroupG/H
centerC23C2×#6103
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC2×C13×#432C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC42×C13C24
hypercenterC2×#432D13
hypocenterC13C2×#1531
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

1050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 137499);