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C17×ΓL(1,𝔽8)×C11⋊C5 #34087284

order19635
automorphism?
homologyAbelianization (H1) = C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×ΓL(1,𝔽8)×C11⋊C5
unambiguous semidirect productC7⋊(C3×C17×C11⋊C5)
unambiguous semidirect productC11⋊(C5×C17×ΓL(1,𝔽8))
unambiguous semidirect product(C7×C17)⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×C17)⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(C11×ΓL(1,𝔽8))⋊(C5×C17)
unambiguous semidirect product(C7×C11⋊C5)⋊(C3×C17)
unambiguous semidirect product(C11×C17×ΓL(1,𝔽8))⋊C5
unambiguous semidirect product(C7×C17×C11⋊C5)⋊C3

Splittings

Fitting, socle, HallC7×C11×C17 ⋊ C3×C5
derived, HallC7×C11 ⋊ C3×C5×C17
HallC7×C17×C11⋊C5 ⋊ C3
HallC11×C17×ΓL(1,𝔽8) ⋊ C5
HallC7×C11⋊C5 ⋊ C3×C17
HallC11×ΓL(1,𝔽8) ⋊ C5×C17
HallC11×C17 ⋊ C5×ΓL(1,𝔽8)
HallC7×C17 ⋊ C3×C11⋊C5
SylowC11 ⋊ C5×C17×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C17×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC17ΓL(1,𝔽8)×C11⋊C5
commutator, cosocle, hypocenterC7×C11C3×C5×C17
FrattiniC1G
Fitting, socleC7×C11×C17C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1309

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19635, 4);