Finite Group Databasebeta

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C3×D5775 #46831445

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

Aliases

direct productC3×D5775
unambiguous semidirect productC3⋊(C3×D1925)
unambiguous semidirect productC11⋊(C3×D525)
unambiguous semidirect productC25⋊(C3×D231)

Splittings

Fitting, HallC32×C7×C11×C25 ⋊ C2
derivedC3×C7×C11×C25 ⋊ C2×C3
HallC32×C11×C25 ⋊ D7
HallC7×C11×C25 ⋊ C3×D3
HallC32×C7×C25 ⋊ D11
HallC32×C7×C11 ⋊ D25
HallC11×C25 ⋊ C3×D21
HallC32×C25 ⋊ D77
HallC7×C25 ⋊ C3×D33
HallC32×C11 ⋊ D175
HallC7×C11 ⋊ C3×D75
HallC32×C7 ⋊ D275
SylowC25 ⋊ C3×D231
SylowC11 ⋊ C3×D525
SylowC32 ⋊ D1925
SylowC7 ⋊ C3×D825

Subgroups

subgroupG/H
center, hypercenterC3D5775
commutator, cosocle, hypocenterC3×C7×C11×C25C2×C3
FrattiniC5C3×D1155
FittingC32×C7×C11×C25C2
socleC32×C5×C7×C11D5
LCSG ▷ C3×C7×C11×C25
UCSC1 ◁ C3

108 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 50 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

8667 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 88);