Finite Group Databasebeta

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C3×C11×D525 #46831444

order34650
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D525
unambiguous semidirect productC3⋊(C3×C11×D175)
unambiguous semidirect productC25⋊(C3×C11×D21)

Splittings

Fitting, HallC32×C7×C11×C25 ⋊ C2
derivedC3×C7×C25 ⋊ C2×C3×C11
HallC32×C11×C25 ⋊ D7
HallC7×C11×C25 ⋊ C3×D3
HallC32×C7×C25 ⋊ C2×C11
HallC32×C7×C11 ⋊ D25
HallC11×C25 ⋊ C3×D21
HallC32×C25 ⋊ C11×D7
HallC7×C25 ⋊ C3×D3×C11
HallC32×C11 ⋊ D175
HallC7×C11 ⋊ C3×D75
HallC32×C7 ⋊ C11×D25
SylowC25 ⋊ C3×C11×D21
SylowC32 ⋊ C11×D175
SylowC7 ⋊ C3×C11×D75

Subgroups

subgroupG/H
center, hypercenterC3×C11D525
commutator, cosocle, hypocenterC3×C7×C25C2×C3×C11
FrattiniC5C3×C11×D105
FittingC32×C7×C11×C25C2
socleC32×C5×C7×C11D5
LCSG ▷ C3×C7×C25
UCSC1 ◁ C3×C11

108 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 11550

Conjugacy classes & character table

8712 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 87);