Finite Group Databasebeta

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C11×D7×D117 #49114482

order36036
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D7×D117
unambiguous semidirect product(C9×D7)⋊(C11×D13)
unambiguous semidirect product(C13×D7)⋊(C11×D9)

Splittings

Fitting, HallC7×C9×C11×C13 ⋊ C22
derived, HallC7×C9×C13 ⋊ C22×C11
HallC9×C11×C13 ⋊ C2×D7
HallC7×C11×C13 ⋊ C2×D9
HallC7×C9×C11 ⋊ C2×D13
HallC11×C13 ⋊ D7×D9
HallC9×C13 ⋊ C2×C11×D7
HallC9×C11 ⋊ D7×D13
HallC7×C13 ⋊ C2×C11×D9
HallC7×C11 ⋊ C2×D117
HallC7×C9 ⋊ C2×C11×D13
SylowC13 ⋊ C11×D7×D9
SylowC9 ⋊ C11×D7×D13
SylowC7 ⋊ C2×C11×D117

Subgroups

subgroupG/H
center, hypercenterC11D7×D117
commutator, cosocle, hypocenterC7×C9×C13C22×C11
FrattiniC3C11×D7×D39
FittingC7×C9×C11×C13C22
socleC3×C7×C11×C13C2×D3
LCSG ▷ C7×C9×C13
UCSC1 ◁ C11

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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) = 9009

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 150);