Finite Group Databasebeta

← Prev (#44528043) Next (#44528045) →

C19×C3⋊D273 #44528044

order31122
automorphism?
homologyAbelianization (H1) = C2×C19 · Schur multiplier (H2) = C3

Aliases

direct productC19×C3⋊D273
unambiguous semidirect productC3⋊(C19×D273)
unambiguous semidirect productC7⋊(C19×C3⋊D39)
unambiguous semidirect productC13⋊(C19×C3⋊D21)

Splittings

Fitting, socle, HallC32×C7×C13×C19 ⋊ C2
derived, HallC32×C7×C13 ⋊ C2×C19
HallC32×C13×C19 ⋊ D7
HallC7×C13×C19 ⋊ C3⋊D3
HallC32×C7×C19 ⋊ D13
HallC13×C19 ⋊ C3⋊D21
HallC32×C19 ⋊ D91
HallC7×C19 ⋊ C3⋊D39
HallC32×C13 ⋊ D7×C19
HallC7×C13 ⋊ C3⋊D3×C19
HallC32×C7 ⋊ C19×D13
SylowC13 ⋊ C19×C3⋊D21
SylowC32 ⋊ C19×D91
SylowC7 ⋊ C19×C3⋊D39

Subgroups

subgroupG/H
center, hypercenterC19C3⋊D273
commutator, cosocle, hypocenterC32×C7×C13C2×C19
FrattiniC1G
Fitting, socleC32×C7×C13×C19C2
LCSG ▷ C32×C7×C13
UCSC1 ◁ C19

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15561

Conjugacy classes & character table

7809 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 527);