Finite Group Databasebeta

C13×#4294⋊D7 #44527599

order31122
automorphism?
homologyAbelianization (H1) = C2×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×#4294⋊D7
unambiguous semidirect product#4294⋊(C13×D7)

Splittings

derived, HallC7×C19 ⋊ C2×C9×C13
HallC7×C13×#4294 ⋊ C2
HallC13×D133 ⋊ C9
HallC13×#4294 ⋊ D7
HallC7×C13×C19 ⋊ C2×C9
HallC7×#4294 ⋊ C2×C13
HallD133 ⋊ C9×C13
HallC13×C19 ⋊ C9×D7
Hall#4294 ⋊ C13×D7
HallC7×C13 ⋊ #4294⋊C2
SylowC19 ⋊ C9×C13×D7
SylowC7 ⋊ C13×#4294⋊C2

Subgroups

subgroupG/H
center, hypercenterC3×C13(C19⋊C3)⋊D7
commutator, hypocenterC7×C19C2×C9×C13
FrattiniC3C13×(C19⋊C3)⋊D7
Fitting, socleC3×C7×C13×C19C2×C3
prime radicalC3×C13×D133C3
cosocleC3×C7×C19C2×C3×C13
LCSG ▷ C7×C19
UCSC1 ◁ C3×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15561

Conjugacy classes & character table

1404 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 82);