Finite Group Databasebeta

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C19×D561 #36319271

order21318
automorphism?
homologyAbelianization (H1) = C2×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×D561
unambiguous semidirect productC3⋊(C19×D187)
unambiguous semidirect productC11⋊(C19×D51)
unambiguous semidirect productC17⋊(C19×D33)

Splittings

Fitting, socle, HallC3×C11×C17×C19 ⋊ C2
derived, HallC3×C11×C17 ⋊ C2×C19
HallC11×C17×C19 ⋊ D3
HallC3×C17×C19 ⋊ D11
HallC3×C11×C19 ⋊ D17
HallC17×C19 ⋊ D33
HallC11×C19 ⋊ D51
HallC11×C17 ⋊ D3×C19
HallC3×C19 ⋊ D187
HallC3×C17 ⋊ C19×D11
HallC3×C11 ⋊ C19×D17
SylowC17 ⋊ C19×D33
SylowC11 ⋊ C19×D51
SylowC3 ⋊ C19×D187

Subgroups

subgroupG/H
center, hypercenterC19D561
commutator, cosocle, hypocenterC3×C11×C17C2×C19
FrattiniC1G
Fitting, socleC3×C11×C17×C19C2
LCSG ▷ C3×C11×C17
UCSC1 ◁ C19

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10659

Conjugacy classes & character table

5358 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21318, 16);