Finite Group Databasebeta

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C9×C11⋊C5×D35 #46831469

order34650
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11⋊C5×D35
unambiguous semidirect productC5⋊(C9×D7×C11⋊C5)
unambiguous semidirect product(C9×C11×D35)⋊C5

Splittings

FittingC5×C7×C9×C11 ⋊ C2×C5
derivedC5×C7×C11 ⋊ C2×C5×C9
HallC5×C7×C9×C11⋊C5 ⋊ C2
HallC5×C9×C11⋊C5 ⋊ D7
HallC5×C7×C11⋊C5 ⋊ C2×C9
HallC7×C9×C11 ⋊ C5×D5
HallC5×C11⋊C5 ⋊ C9×D7
HallC9×C11 ⋊ C5×D35
HallC7×C11 ⋊ C5×C9×D5
HallC7×C9 ⋊ D5×C11⋊C5
SylowC11 ⋊ C5×C9×D35
SylowC7 ⋊ C9×D5×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC9C11⋊C5×D35
commutator, hypocenterC5×C7×C11C2×C5×C9
FrattiniC3C3×C11⋊C5×D35
FittingC5×C7×C9×C11C2×C5
socle, cosocleC3×C5×C7×C11C2×C3×C5
prime radicalC3×C11⋊C5×D35C3
LCSG ▷ C5×C7×C11
UCSC1 ◁ C9

120 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 45 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) = 3465

Conjugacy classes & character table

1197 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 112);