Finite Group Databasebeta

C13×#6104 #72259260

order2704
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×#6104

Splittings

FittingD4×C132 ⋊ C2
SylowC132 ⋊ D8

Subgroups

subgroupG/H
centerC2×C13C22⋊D13
commutator, cosocleC4×C13C22×C13
FrattiniC4C2×C13×D13
FittingD4×C132C2
socleC2×C132D4
hypercenterD4×C13D13
hypocenterC13C13×D8
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C13 ◁ C4×C13 ◁ D4×C13

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 104

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72259265, C13×#88186, #72259275, …
maximal normal subgroup of#72259265, C13×#88186, #72259275, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.