Finite Group Databasebeta

C2×#13114664 #15860679

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#13114664

Splittings

FittingC2×C4×C13×C4⋊C4 ⋊ C2
SylowC13 ⋊ C2×#1762

Subgroups

subgroupG/H
centerC24C2×C22⋊D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC2×C4×C13×C4⋊C4C2
socleC24×C13C2×D4
prime radicalC23×D52C22
cosocleC22×C4×C13C24
hypercenterC2×C4×C4⋊C4D13
hypocenterC13C2×#1762
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×C4×C4⋊C4

2118 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, 167328);