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C11×C11⋊(ΓL(1,𝔽8)⋊C4) #23778987

order10164
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C11⋊(ΓL(1,𝔽8)⋊C4)
unambiguous semidirect productC11⋊(C11×ΓL(1,𝔽8)⋊C4)
unambiguous semidirect productΓL(1,𝔽8)⋊(C11×Dic11)
unambiguous semidirect productDic77⋊(C3×C11)
unambiguous semidirect product(C11×Dic77)⋊C3

Splittings

derivedC7×C11 ⋊ C3×C4×C11
HallC11×Dic77 ⋊ C3
HallC112×ΓL(1,𝔽8) ⋊ C4
HallC7×C112 ⋊ C3×C4
SylowC112 ⋊ ΓL(1,𝔽8)⋊C4
HallΓL(1,𝔽8) ⋊ C11×Dic11
SylowC7 ⋊ C3×C11×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C11C11⋊AGL(1,𝔽7)
commutator, hypocenterC7×C11C3×C4×C11
FrattiniC2C11×C11⋊AGL(1,𝔽7)
Fitting, socleC2×C7×C112C2×C3
prime radicalC2×C112×ΓL(1,𝔽8)C2
cosocleC2×C7×C11C2×C3×C11
LCSG ▷ C7×C11
UCSC1 ◁ C2×C11

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

704 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)⋊#13089712, C3×C11×C11⋊(ΓL(1,𝔽8)⋊C4), C11×C3⋊(C11⋊(ΓL(1,𝔽8)⋊C4))
maximal normal subgroup ofC3×C11×C11⋊(ΓL(1,𝔽8)⋊C4)
maximal quotient ofC11×C11⋊(Dic7⋊C9), C3×C11×C11⋊(ΓL(1,𝔽8)⋊C4), C11×C3⋊(C11⋊(ΓL(1,𝔽8)⋊C4))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10164, 39);