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C3×D5×C11×ΓL(1,𝔽8) #20294175

order6930
automorphism?
homologyAbelianization (H1) = C2×C32×C11 · Schur multiplier (H2) = C3

Aliases

direct productC3×D5×C11×ΓL(1,𝔽8)
unambiguous semidirect productC5⋊(C2×C3×C11×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D5)⋊(C32×C11)
unambiguous semidirect product(C3×C7×D5)⋊(C3×C11)
unambiguous semidirect product(C7×D5×C11)⋊C32
unambiguous semidirect product(C3×C7×D5×C11)⋊C3

Splittings

Fitting, socleC3×C5×C7×C11 ⋊ C2×C3
derived, HallC5×C7 ⋊ C2×C32×C11
HallC3×C5×C11×ΓL(1,𝔽8) ⋊ C2
HallC7×D5×C11 ⋊ C32
HallC5×C7×C11 ⋊ C2×C32
HallC3×C5×ΓL(1,𝔽8) ⋊ C2×C11
HallC7×C11 ⋊ C32×D5
HallC7×D5 ⋊ C32×C11
HallC5×C11 ⋊ C2×C3×ΓL(1,𝔽8)
SylowC7 ⋊ C32×D5×C11
SylowC5 ⋊ C2×C3×C11×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC3×C11D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C2×C32×C11
FrattiniC1G
Fitting, socleC3×C5×C7×C11C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C3×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C3×C11⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5)), C3×C11×AGL(1,𝔽5)×ΓL(1,𝔽8), …
maximal normal subgroup ofC3×C11×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C3×C11⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5)), C3×C11×AGL(1,𝔽5)×ΓL(1,𝔽8), …
maximal quotient ofC3×C11×Dic5×ΓL(1,𝔽8), C2×C3×D5×C11×ΓL(1,𝔽8), C3×C11×ΓL(1,𝔽8)×D25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 62);