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D7×D561 #30628155

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

Aliases

direct productD7×D561
unambiguous semidirect product(C3×D7)⋊D187
unambiguous semidirect product(C11×D7)⋊D51
unambiguous semidirect product(D7×C17)⋊D33

Splittings

Fitting, socle, derived, HallC3×C7×C11×C17 ⋊ C22
HallC7×C11×C17 ⋊ C2×D3
HallC3×C11×C17 ⋊ C2×D7
HallC3×C7×C17 ⋊ C2×D11
HallC3×C7×C11 ⋊ C2×D17
HallC11×C17 ⋊ D3×D7
HallC7×C17 ⋊ C2×D33
HallC7×C11 ⋊ C2×D51
HallC3×C17 ⋊ D7×D11
HallC3×C11 ⋊ D7×D17
HallC3×C7 ⋊ C2×D187
SylowC17 ⋊ D7×D33
SylowC11 ⋊ D7×D51
SylowC7 ⋊ C2×D561
SylowC3 ⋊ D7×D187

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C17C22
LCSG ▷ C3×C7×C11×C17
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3927

Conjugacy classes & character table

1410 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 76);