Finite Group Databasebeta

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C11×#4296⋊D7 #39911847

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

Aliases

direct productC11×#4296⋊D7
unambiguous semidirect product#4296⋊(C11×D7)

Splittings

Fitting, socle, HallC7×C11×C19 ⋊ C2×C9
derived, HallC7×C19 ⋊ C2×C9×C11
HallC7×C11×#4296 ⋊ C2
HallC11×D133 ⋊ C9
HallC11×#4296 ⋊ D7
HallC7×#4296 ⋊ C2×C11
HallD133 ⋊ C9×C11
HallC11×C19 ⋊ C9×D7
Hall#4296 ⋊ C11×D7
HallC7×C11 ⋊ AGL(1,𝔽19)
SylowC19 ⋊ C9×C11×D7
SylowC7 ⋊ C11×AGL(1,𝔽19)

Subgroups

subgroupG/H
center, hypercenterC11#4296⋊D7
commutator, hypocenterC7×C19C2×C9×C11
FrattiniC1G
Fitting, socleC7×C11×C19C2×C9
prime radicalC11×(C19⋊C3)⋊D7C3
cosocleC7×C19⋊C3C2×C3×C11
LCSG ▷ C7×C19
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1463

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26334, 74);