Finite Group Databasebeta

D13×#3105 #16730960

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productD13×#3105

Splittings

FittingC13×#3105 ⋊ C2
SylowC13 ⋊ C2×#3105

Subgroups

subgroupG/H
centerC2×C4C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC13×#3105C2
socleC22×C13C23×D4
prime radicalD13×#447C2
hypercenter#3105D13
hypocenterC13C2×#3105
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3105

2602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1037609);