Finite Group Databasebeta

← Prev (#34035185) Next (#34035187) →

C17×(C11⋊C5)⋊AGL(1,𝔽5) #34035186

order18700
automorphism?
homologyAbelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×(C11⋊C5)⋊AGL(1,𝔽5)
unambiguous semidirect product(C11⋊C5)⋊(C17×AGL(1,𝔽5))
unambiguous semidirect product(C11⋊AGL(1,𝔽5))⋊(C5×C17)
unambiguous semidirect product(C17×C11⋊AGL(1,𝔽5))⋊C5

Splittings

Fitting, socleC5×C11×C17 ⋊ C4×C5
derivedC5×C11 ⋊ C4×C5×C17
HallC5×C17×C11⋊C5 ⋊ C4
HallC5×C11⋊C5 ⋊ C4×C17
HallC11×C17 ⋊ C5×AGL(1,𝔽5)
SylowC11 ⋊ C5×C17×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC17(C11⋊C5)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C4×C5×C17
FrattiniC1G
Fitting, socleC5×C11×C17C4×C5
prime radicalD5×C17×C11⋊C5C2
cosocleD5×C11C2×C5×C17
LCSG ▷ C5×C11
UCSC1 ◁ C17

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 935

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18700, 71);