Finite Group Databasebeta

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C3×C7×C11×D75 #46831442

order34650
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C11×D75
unambiguous semidirect productC3⋊(C3×C7×C11×D25)
unambiguous semidirect productC25⋊(C3×D3×C7×C11)

Splittings

Fitting, HallC32×C7×C11×C25 ⋊ C2
derivedC3×C25 ⋊ C2×C3×C7×C11
HallC32×C11×C25 ⋊ C2×C7
HallC7×C11×C25 ⋊ C3×D3
HallC32×C7×C25 ⋊ C2×C11
HallC32×C7×C11 ⋊ D25
HallC11×C25 ⋊ C3×D3×C7
HallC32×C25 ⋊ C2×C7×C11
HallC7×C25 ⋊ C3×D3×C11
HallC32×C11 ⋊ C7×D25
HallC32×C7 ⋊ C11×D25
SylowC25 ⋊ C3×D3×C7×C11
SylowC32 ⋊ C7×C11×D25

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11D75
commutator, cosocle, hypocenterC3×C25C2×C3×C7×C11
FrattiniC5C3×C7×C11×D15
FittingC32×C7×C11×C25C2
socleC32×C5×C7×C11D5
LCSG ▷ C3×C25
UCSC1 ◁ C3×C7×C11

108 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 56 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

9009 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 85);