Finite Group Databasebeta

← Prev (#39911791) Next (#39911793) →

C19×D693 #39911792

order26334
automorphism?
homologyAbelianization (H1) = C2×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×D693
unambiguous semidirect productC7⋊(C19×D99)
unambiguous semidirect productC9⋊(C19×D77)
unambiguous semidirect productC11⋊(C19×D63)

Splittings

Fitting, HallC7×C9×C11×C19 ⋊ C2
derived, HallC7×C9×C11 ⋊ C2×C19
HallC9×C11×C19 ⋊ D7
HallC7×C11×C19 ⋊ D9
HallC7×C9×C19 ⋊ D11
HallC11×C19 ⋊ D63
HallC9×C19 ⋊ D77
HallC7×C19 ⋊ D99
HallC9×C11 ⋊ D7×C19
HallC7×C11 ⋊ D9×C19
HallC7×C9 ⋊ C19×D11
SylowC11 ⋊ C19×D63
SylowC9 ⋊ C19×D77
SylowC7 ⋊ C19×D99

Subgroups

subgroupG/H
center, hypercenterC19D693
commutator, cosocle, hypocenterC7×C9×C11C2×C19
FrattiniC3C19×D231
FittingC7×C9×C11×C19C2
socleC3×C7×C11×C19D3
LCSG ▷ C7×C9×C11
UCSC1 ◁ C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13167

Conjugacy classes & character table

6612 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26334, 19);