Finite Group Databasebeta

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C2×C11⋊((C19⋊C3)⋊D13) #45656770

order32604
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11⋊((C19⋊C3)⋊D13)
unambiguous semidirect product(C2×C11)⋊((C19⋊C3)⋊D13)
unambiguous semidirect product(C2×C19⋊C3)⋊D143

Splittings

Fitting, socleC2×C11×C13×C19 ⋊ C2×C3
derived, HallC11×C13×C19 ⋊ C22×C3
HallC2×D2717 ⋊ C3
HallC11×C13×C19⋊C3 ⋊ C22
HallC13×C19⋊C3 ⋊ C2×D11
HallC11×C19⋊C3 ⋊ C2×D13
HallC13×C19 ⋊ C2×C3×D11
HallC11×C19 ⋊ C2×C3×D13
HallC11×C13 ⋊ C2×D19⋊C3
HallC19⋊C3 ⋊ C2×D143
SylowC19 ⋊ C2×C3×D143
SylowC13 ⋊ C2×C11⋊(D19⋊C3)
SylowC11 ⋊ C2×(C19⋊C3)⋊D13

Subgroups

subgroupG/H
center, hypercenterC2C11⋊((C19⋊C3)⋊D13)
commutator, cosocle, hypocenterC11×C13×C19C22×C3
FrattiniC1G
Fitting, socleC2×C11×C13×C19C2×C3
LCSG ▷ C11×C13×C19
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5434

Conjugacy classes & character table

1296 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 120);