Finite Group Databasebeta

C17×C11⋊(D7⋊C9) #37555629

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

Aliases

direct productC17×C11⋊(D7⋊C9)
unambiguous semidirect productC11⋊(C17×D7⋊C9)
unambiguous semidirect product(C7⋊C9)⋊(C17×D11)
unambiguous semidirect productD77⋊(C9×C17)
unambiguous semidirect product(C17×D77)⋊C9

Splittings

derived, HallC7×C11 ⋊ C2×C9×C17
HallC11×C17×C7⋊C9 ⋊ C2
HallC17×D77 ⋊ C9
HallC7×C11×C17 ⋊ C2×C9
HallC17×C7⋊C9 ⋊ D11
HallC11×C7⋊C9 ⋊ C2×C17
HallC11×C17 ⋊ D7⋊C9
HallD77 ⋊ C9×C17
HallC7×C17 ⋊ C9×D11
HallC7⋊C9 ⋊ C17×D11
SylowC11 ⋊ C17×D7⋊C9
SylowC7 ⋊ C9×C17×D11

Subgroups

subgroupG/H
center, hypercenterC3×C17C11⋊AGL(1,𝔽7)
commutator, hypocenterC7×C11C2×C9×C17
FrattiniC3C17×C11⋊AGL(1,𝔽7)
Fitting, socleC3×C7×C11×C17C2×C3
prime radicalC3×C17×D77C3
cosocleC3×C7×C11C2×C3×C17
LCSG ▷ C7×C11
UCSC1 ◁ C3×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

1632 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 23);