Finite Group Databasebeta

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C11×D15⋊D49 #44568415

order32340
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D15⋊D49
unambiguous semidirect productD15⋊(C11×D49)
unambiguous semidirect productD147⋊(D5×C11)
unambiguous semidirect productD245⋊(D3×C11)

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C22
derived, HallC3×C5×C49 ⋊ C22×C11
HallC5×C11×C49 ⋊ C2×D3
HallC3×C11×C49 ⋊ C2×D5
HallC11×C49 ⋊ D3×D5
HallC5×C49 ⋊ C2×D3×C11
HallC3×C5×C11 ⋊ C2×D49
HallC3×C49 ⋊ C2×D5×C11
HallC5×C11 ⋊ D3×D49
SylowC49 ⋊ D3×D5×C11
HallC3×C11 ⋊ D5×D49
HallC3×C5 ⋊ C2×C11×D49
SylowC5 ⋊ D3×C11×D49
SylowC3 ⋊ D5×C11×D49

Subgroups

subgroupG/H
center, hypercenterC11D15⋊D49
commutator, cosocle, hypocenterC3×C5×C49C22×C11
FrattiniC7C11×D15⋊D7
FittingC3×C5×C11×C49C22
socleC3×C5×C7×C11C2×D7
LCSG ▷ C3×C5×C49
UCSC1 ◁ C11

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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

2508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 117);