Finite Group Databasebeta

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D3×C11⋊C5×D49 #44568346

order32340
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD3×C11⋊C5×D49
unambiguous semidirect product(D3×C49)⋊(C2×C11⋊C5)
unambiguous semidirect product(C3×D49)⋊(C2×C11⋊C5)
unambiguous semidirect productD147⋊(C2×C11⋊C5)
unambiguous semidirect product(D3×C11×D49)⋊C5

Splittings

Fitting, derived, HallC3×C11×C49 ⋊ C22×C5
HallC3×C49×C11⋊C5 ⋊ C22
HallD3×C11×D49 ⋊ C5
HallC49×C11⋊C5 ⋊ C2×D3
HallC11×C49 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C2×D49
HallC3×C49 ⋊ C22×C11⋊C5
SylowC49 ⋊ C2×D3×C11⋊C5
HallC3×C11 ⋊ C2×C5×D49
SylowC11 ⋊ C5×D3×D49
SylowC3 ⋊ C2×C11⋊C5×D49

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C11×C49C22×C5
FrattiniC7D3×D7×C11⋊C5
socleC3×C7×C11C2×C5×D7
LCSG ▷ C3×C11×C49
UCSC1

120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1617

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 48);