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C3×C11×ΓL(1,𝔽8)⋊Dic5 #28357495

order13860
isoclinismisoclinic class of C5⋊AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C32×C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11×ΓL(1,𝔽8)⋊Dic5
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×C11×Dic5)
unambiguous semidirect productDic35⋊(C32×C11)
unambiguous semidirect product(C3×Dic35)⋊(C3×C11)
unambiguous semidirect product(C11×Dic35)⋊C32
unambiguous semidirect product(C3×C11×Dic35)⋊C3

Splittings

derived, HallC5×C7 ⋊ C32×C4×C11
HallC3×C5×C11×ΓL(1,𝔽8) ⋊ C4
HallC11×Dic35 ⋊ C32
HallC3×C11×ΓL(1,𝔽8) ⋊ Dic5
HallC5×C7×C11 ⋊ C32×C4
HallC3×C5×ΓL(1,𝔽8) ⋊ C4×C11
HallDic35 ⋊ C32×C11
HallC7×C11 ⋊ C32×Dic5
HallC3×ΓL(1,𝔽8) ⋊ C11×Dic5
HallC5×C11 ⋊ C3×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C32×C11×Dic5
SylowC5 ⋊ C3×C11×ΓL(1,𝔽8)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11C5⋊AGL(1,𝔽7)
commutator, hypocenterC5×C7C32×C4×C11
FrattiniC2C3×C11×C5⋊AGL(1,𝔽7)
Fitting, socleC2×C3×C5×C7×C11C2×C3
prime radicalC2×C3×C5×C11×ΓL(1,𝔽8)C2
cosocleC2×C5×C7C2×C32×C11
LCSG ▷ C5×C7
UCSC1 ◁ C2×C3×C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

1122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 162);