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C2×C17×ΓL(1,𝔽8)×D11 #30628121

order15708
automorphism?
homologyAbelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×ΓL(1,𝔽8)×D11
unambiguous semidirect productC11⋊(C22×C17×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C11)⋊(C2×C17×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C7×D11)⋊(C3×C17)
unambiguous semidirect product(C2×C7×C17×D11)⋊C3

Splittings

Fitting, socleC2×C7×C11×C17 ⋊ C2×C3
derived, HallC7×C11 ⋊ C22×C3×C17
HallC2×C7×C17×D11 ⋊ C3
HallC11×C17×ΓL(1,𝔽8) ⋊ C22
HallC7×C11×C17 ⋊ C22×C3
HallC2×C7×D11 ⋊ C3×C17
HallC11×ΓL(1,𝔽8) ⋊ C22×C17
HallC11×C17 ⋊ C22×ΓL(1,𝔽8)
HallC7×C17 ⋊ C2×C3×D11
SylowC11 ⋊ C22×C17×ΓL(1,𝔽8)
SylowC7 ⋊ C2×C3×C17×D11

Subgroups

subgroupG/H
center, hypercenterC2×C17ΓL(1,𝔽8)×D11
commutator, cosocle, hypocenterC7×C11C22×C3×C17
FrattiniC1G
Fitting, socleC2×C7×C11×C17C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C2×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2618

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 42);