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C3×C11⋊C5×ΓL(1,𝔽8)⋊C4 #28357474

order13860
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11⋊C5×ΓL(1,𝔽8)⋊C4
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×C4×C11⋊C5)
unambiguous semidirect productDic7⋊(C32×C11⋊C5)
unambiguous semidirect product(C3×Dic7)⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×ΓL(1,𝔽8)⋊C4)⋊(C3×C5)
unambiguous semidirect product(Dic7×C11⋊C5)⋊C32
unambiguous semidirect product(C3×C11×ΓL(1,𝔽8)⋊C4)⋊C5
unambiguous semidirect product(C3×Dic7×C11⋊C5)⋊C3

Splittings

derived, HallC7×C11 ⋊ C32×C4×C5
HallC3×ΓL(1,𝔽8)×C11⋊C5 ⋊ C4
HallC3×C11×ΓL(1,𝔽8)⋊C4 ⋊ C5
HallDic7×C11⋊C5 ⋊ C32
HallC3×C11×ΓL(1,𝔽8) ⋊ C4×C5
HallC7×C11⋊C5 ⋊ C32×C4
HallC11×Dic7 ⋊ C32×C5
HallC3×ΓL(1,𝔽8) ⋊ C4×C11⋊C5
HallDic7 ⋊ C32×C11⋊C5
SylowC11 ⋊ C3×C5×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C32×C4×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3AGL(1,𝔽7)×C11⋊C5
commutator, hypocenterC7×C11C32×C4×C5
FrattiniC2C3×AGL(1,𝔽7)×C11⋊C5
Fitting, socleC2×C3×C7×C11C2×C3×C5
prime radicalC2×C3×ΓL(1,𝔽8)×C11⋊C5C2
cosocleC2×C7×C11C2×C32×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 924

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 141);