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D11×D357 #30628147

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

Aliases

direct productD11×D357
unambiguous semidirect product(C3×D11)⋊D119
unambiguous semidirect product(C7×D11)⋊D51
unambiguous semidirect product(C17×D11)⋊D21

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 ⋊ C2×D21
HallC7×C17 ⋊ D3×D11
HallC7×C11 ⋊ C2×D51
HallC3×C17 ⋊ D7×D11
HallC3×C11 ⋊ C2×D119
HallC3×C7 ⋊ D11×D17
SylowC17 ⋊ D11×D21
SylowC11 ⋊ C2×D357
SylowC7 ⋊ D11×D51
SylowC3 ⋊ D11×D119

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

1260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 68);