Finite Group Databasebeta

C2×#13115291 #15864703

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#13115291

Splittings

SylowC13 ⋊ C2×#1899

Subgroups

subgroupG/H
centerC23C22⋊C4×D13
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC22×C13×#99C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D4×C13C22
cosocleC24×C13C24
hypercenterC22×#99D13
hypocenterC13C2×#1899
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

2066 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 171352);