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C2×ΓL(1,𝔽8)×D187 #30628122

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

Aliases

direct productC2×ΓL(1,𝔽8)×D187
unambiguous semidirect product(C2×C11)⋊(ΓL(1,𝔽8)×D17)
unambiguous semidirect product(C2×C17)⋊(ΓL(1,𝔽8)×D11)
unambiguous semidirect product(C2×C7×D187)⋊C3

Splittings

Fitting, socleC2×C7×C11×C17 ⋊ C2×C3
derived, HallC7×C11×C17 ⋊ C22×C3
HallC2×C7×D187 ⋊ C3
HallC11×C17×ΓL(1,𝔽8) ⋊ C22
HallC17×ΓL(1,𝔽8) ⋊ C2×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×D17
HallC11×C17 ⋊ C22×ΓL(1,𝔽8)
HallC7×C17 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D17
SylowC17 ⋊ C2×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C2×ΓL(1,𝔽8)×D17
SylowC7 ⋊ C2×C3×D187

Subgroups

subgroupG/H
center, hypercenterC2ΓL(1,𝔽8)×D187
commutator, cosocle, hypocenterC7×C11×C17C22×C3
FrattiniC1G
Fitting, socleC2×C7×C11×C17C2×C3
LCSG ▷ C7×C11×C17
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2618

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 43);