Finite Group Databasebeta

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D49×D165 #44568400

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

Aliases

direct productD49×D165
unambiguous semidirect product(C3×D49)⋊D55
unambiguous semidirect product(C5×D49)⋊D33
unambiguous semidirect product(C11×D49)⋊D15

Splittings

Fitting, derived, HallC3×C5×C11×C49 ⋊ C22
HallC5×C11×C49 ⋊ C2×D3
HallC3×C11×C49 ⋊ C2×D5
HallC3×C5×C49 ⋊ C2×D11
HallC11×C49 ⋊ C2×D15
HallC5×C49 ⋊ C2×D33
HallC3×C5×C11 ⋊ C2×D49
HallC3×C49 ⋊ C2×D55
HallC5×C11 ⋊ D3×D49
SylowC49 ⋊ C2×D165
HallC3×C11 ⋊ D5×D49
HallC3×C5 ⋊ D11×D49
SylowC11 ⋊ D15×D49
SylowC5 ⋊ D33×D49
SylowC3 ⋊ D49×D55

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C5×C11×C49C22
FrattiniC7D7×D165
socleC3×C5×C7×C11C2×D7
LCSG ▷ C3×C5×C11×C49
UCSC1

120 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 37 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) = 8085

Conjugacy classes & character table

2184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 102);