Finite Group Databasebeta

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C11×C17×D7⋊C9 #37555627

order23562
automorphism?
homologyAbelianization (H1) = C2×C9×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC11×C17×D7⋊C9
unambiguous semidirect productD7⋊(C9×C11×C17)
unambiguous semidirect product(C7⋊C9)⋊(C2×C11×C17)
unambiguous semidirect product(C11×D7)⋊(C9×C17)
unambiguous semidirect product(D7×C17)⋊(C9×C11)
unambiguous semidirect product(C11×D7×C17)⋊C9

Splittings

derived, SylowC7 ⋊ C2×C9×C11×C17
HallC11×C17×C7⋊C9 ⋊ C2
HallC11×D7×C17 ⋊ C9
HallC7×C11×C17 ⋊ C2×C9
HallC17×C7⋊C9 ⋊ C2×C11
HallC11×C7⋊C9 ⋊ C2×C17
HallD7×C17 ⋊ C9×C11
HallC11×D7 ⋊ C9×C17
HallC7×C17 ⋊ C2×C9×C11
HallC7×C11 ⋊ C2×C9×C17
HallC7⋊C9 ⋊ C2×C11×C17
HallD7 ⋊ C9×C11×C17

Subgroups

subgroupG/H
center, hypercenterC3×C11×C17AGL(1,𝔽7)
commutator, hypocenterC7C2×C9×C11×C17
FrattiniC3C11×C17×AGL(1,𝔽7)
Fitting, socleC3×C7×C11×C17C2×C3
prime radicalC3×C11×D7×C17C3
cosocleC3×C7C2×C3×C11×C17
LCSG ▷ C7
UCSC1 ◁ C3×C11×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

3927 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 21);