Finite Group Databasebeta

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C11×C17×D19⋊C3 #36319273

order21318
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC11×C17×D19⋊C3
unambiguous semidirect productD19⋊(C3×C11×C17)
unambiguous semidirect product(C19⋊C3)⋊(C2×C11×C17)
unambiguous semidirect product(C11×D19)⋊(C3×C17)
unambiguous semidirect product(C17×D19)⋊(C3×C11)
unambiguous semidirect product(C11×C17×D19)⋊C3

Splittings

Fitting, socle, HallC11×C17×C19 ⋊ C2×C3
derived, SylowC19 ⋊ C2×C3×C11×C17
HallC11×C17×C19⋊C3 ⋊ C2
HallC11×C17×D19 ⋊ C3
HallC17×C19⋊C3 ⋊ C2×C11
HallC17×D19 ⋊ C3×C11
HallC11×C19⋊C3 ⋊ C2×C17
HallC11×D19 ⋊ C3×C17
HallC17×C19 ⋊ C2×C3×C11
HallC11×C19 ⋊ C2×C3×C17
HallC19⋊C3 ⋊ C2×C11×C17
HallD19 ⋊ C3×C11×C17

Subgroups

subgroupG/H
center, hypercenterC11×C17D19⋊C3
commutator, cosocle, hypocenterC19C2×C3×C11×C17
FrattiniC1G
Fitting, socleC11×C17×C19C2×C3
LCSG ▷ C19
UCSC1 ◁ C11×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3553

Conjugacy classes & character table

1683 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21318, 18);