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C11×D7×D51 #30628151

order15708
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D7×D51
unambiguous semidirect product(C3×D7)⋊(C11×D17)
unambiguous semidirect product(D7×C17)⋊(D3×C11)

Splittings

Fitting, socle, HallC3×C7×C11×C17 ⋊ C22
derived, HallC3×C7×C17 ⋊ C22×C11
HallC7×C11×C17 ⋊ C2×D3
HallC3×C11×C17 ⋊ C2×D7
HallC3×C7×C11 ⋊ C2×D17
HallC11×C17 ⋊ D3×D7
HallC7×C17 ⋊ C2×D3×C11
HallC7×C11 ⋊ C2×D51
HallC3×C17 ⋊ C2×C11×D7
HallC3×C11 ⋊ D7×D17
HallC3×C7 ⋊ C2×C11×D17
SylowC17 ⋊ D3×C11×D7
SylowC7 ⋊ C2×C11×D51
SylowC3 ⋊ C11×D7×D17

Subgroups

subgroupG/H
center, hypercenterC11D7×D51
commutator, cosocle, hypocenterC3×C7×C17C22×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C17C22
LCSG ▷ C3×C7×C17
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3927

Conjugacy classes & character table

1485 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 72);