Finite Group Databasebeta

C2×#13123501 #16726681

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×#13123501

Splittings

FittingC22×C13×C4⋊C8 ⋊ C2
SylowC13 ⋊ C2×#2925

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C13×C4⋊C8C2
socleC23×C13C23×C4
prime radicalC22×#6127C22
cosocleC2×C4×C13C25
hypercenterC22×C4⋊C8D13
hypocenterC13C2×#2925
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C4⋊C8

2178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033330);