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C3×D17×D77 #30628129

order15708
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D17×D77
unambiguous semidirect product(C11×D17)⋊(C3×D7)

Splittings

Fitting, socle, HallC3×C7×C11×C17 ⋊ C22
derived, HallC7×C11×C17 ⋊ C22×C3
HallC3×C11×C17 ⋊ C2×D7
HallC3×C7×C17 ⋊ C2×D11
HallC3×C7×C11 ⋊ C2×D17
HallC11×C17 ⋊ C2×C3×D7
HallC7×C17 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D17
HallC3×C17 ⋊ C2×D77
HallC3×C11 ⋊ D7×D17
HallC3×C7 ⋊ D11×D17
SylowC17 ⋊ C2×C3×D77
SylowC11 ⋊ C3×D7×D17
SylowC7 ⋊ C3×D11×D17

Subgroups

subgroupG/H
center, hypercenterC3D17×D77
commutator, cosocle, hypocenterC7×C11×C17C22×C3
FrattiniC1G
Fitting, socleC3×C7×C11×C17C22
LCSG ▷ C7×C11×C17
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3927

Conjugacy classes & character table

1200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 50);