Finite Group Databasebeta

C2×#13114747 #15862025

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

Aliases

direct productC2×#13114747

Splittings

FittingC22×C13×C22⋊C8 ⋊ C2
SylowC13 ⋊ C2×#1780

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutatorC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×C22⋊C8C2
socleC24×C13C22×C4
prime radicalC23×#6127C2
cosocleC22×C4×C13C24
hypercenterC22×C22⋊C8D13
hypocenterC13C2×#1780
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

4070 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, 168674);