Finite Group Databasebeta

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C11×C19×D7⋊C9 #39911807

order26334
automorphism?
homologyAbelianization (H1) = C2×C9×C11×C19 · Schur multiplier (H2) = C1

Aliases

direct productC11×C19×D7⋊C9
unambiguous semidirect productD7⋊(C9×C11×C19)
unambiguous semidirect product(C7⋊C9)⋊(C2×C11×C19)
unambiguous semidirect product(C11×D7)⋊(C9×C19)

Splittings

derived, SylowC7 ⋊ C2×C9×C11×C19
HallC11×C19×C7⋊C9 ⋊ C2
HallC11×D7×C19 ⋊ C9
HallC7×C11×C19 ⋊ C2×C9
HallC19×C7⋊C9 ⋊ C2×C11
HallC11×C7⋊C9 ⋊ C2×C19
HallD7×C19 ⋊ C9×C11
HallC11×D7 ⋊ C9×C19
HallC7×C19 ⋊ C2×C9×C11
HallC7×C11 ⋊ C2×C9×C19
HallC7⋊C9 ⋊ C2×C11×C19
HallD7 ⋊ C9×C11×C19

Subgroups

subgroupG/H
center, hypercenterC3×C11×C19AGL(1,𝔽7)
commutator, hypocenterC7C2×C9×C11×C19
FrattiniC3C11×C19×AGL(1,𝔽7)
Fitting, socleC3×C7×C11×C19C2×C3
prime radicalC3×C11×D7×C19C3
cosocleC3×C7C2×C3×C11×C19
LCSG ▷ C7
UCSC1 ◁ C3×C11×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13167

Conjugacy classes & character table

4389 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26334, 34);