Finite Group Databasebeta

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C2×C19×D429 #45656837

order32604
automorphism?
homologyAbelianization (H1) = C22×C19 · Schur multiplier (H2) = C2

Aliases

direct productC2×C19×D429
unambiguous semidirect product(C2×C3)⋊(C19×D143)
unambiguous semidirect product(C2×C11)⋊(C19×D39)
unambiguous semidirect product(C2×C13)⋊(C19×D33)

Splittings

Fitting, socleC2×C3×C11×C13×C19 ⋊ C2
derived, HallC3×C11×C13 ⋊ C22×C19
HallC3×C11×C13×C19 ⋊ C22
HallC11×C13×C19 ⋊ C2×D3
HallC3×C13×C19 ⋊ C2×D11
HallC3×C11×C19 ⋊ C2×D13
HallC13×C19 ⋊ C2×D33
HallC11×C19 ⋊ C2×D39
HallC11×C13 ⋊ C2×D3×C19
HallC3×C19 ⋊ C2×D143
HallC3×C13 ⋊ C2×C19×D11
HallC3×C11 ⋊ C2×C19×D13
SylowC13 ⋊ C2×C19×D33
SylowC11 ⋊ C2×C19×D39
SylowC3 ⋊ C2×C19×D143

Subgroups

subgroupG/H
center, hypercenterC2×C19D429
commutator, cosocle, hypocenterC3×C11×C13C22×C19
FrattiniC1G
Fitting, socleC2×C3×C11×C13×C19C2
LCSG ▷ C3×C11×C13
UCSC1 ◁ C2×C19

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16302

Conjugacy classes & character table

8208 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 187);