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C3×ΓL(1,𝔽8)×D187 #37555638

order23562
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×D187
unambiguous semidirect productC11⋊(C3×ΓL(1,𝔽8)×D17)
unambiguous semidirect productC17⋊(C3×ΓL(1,𝔽8)×D11)
unambiguous semidirect product(C7×D187)⋊C32
unambiguous semidirect product(C3×C7×D187)⋊C3

Splittings

Fitting, socleC3×C7×C11×C17 ⋊ C2×C3
derived, HallC7×C11×C17 ⋊ C2×C32
HallC3×C11×C17×ΓL(1,𝔽8) ⋊ C2
HallC7×D187 ⋊ C32
HallC3×C17×ΓL(1,𝔽8) ⋊ D11
HallC3×C11×ΓL(1,𝔽8) ⋊ D17
HallC11×C17 ⋊ C2×C3×ΓL(1,𝔽8)
HallC7×C17 ⋊ C32×D11
HallC7×C11 ⋊ C32×D17
SylowC17 ⋊ C3×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C3×ΓL(1,𝔽8)×D17
SylowC7 ⋊ C32×D187

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)×D187
commutator, cosocle, hypocenterC7×C11×C17C2×C32
FrattiniC1G
Fitting, socleC3×C7×C11×C17C2×C3
LCSG ▷ C7×C11×C17
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3927

Conjugacy classes & character table

1425 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 32);