Finite Group Databasebeta

D13×#2888 #16726410

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD13×#2888

Splittings

FittingC13×#2888 ⋊ C2
SylowC13 ⋊ C2×#2888

Subgroups

subgroupG/H
centerC2C22×C22⋊C4×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC13×#2888C2
socleC2×C13C23×C22⋊C4
prime radicalC2×D13×H(5,𝔽2)C2
cosocleC2×C4×C13C25
hypercenter#2888D13
hypocenterC13C2×#2888
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×#41 ◁ #2888

5114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

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, 1033059);