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ΓL(1,𝔽8)⋊(D67⋊C11) #44526289

order30954
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productΓL(1,𝔽8)⋊(D67⋊C11)
unambiguous semidirect product(ΓL(1,𝔽8)⋊D67)⋊C11

Splittings

Fitting, socle, derived, HallC7×C67 ⋊ C2×C3×C11
HallΓL(1,𝔽8)×C67⋊C11 ⋊ C2
HallC7⋊(D67⋊C11) ⋊ C3
HallC7×C67⋊C11 ⋊ C2×C3
HallΓL(1,𝔽8)⋊D67 ⋊ C11
HallΓL(1,𝔽8)×C67 ⋊ C2×C11
HallD469 ⋊ C3×C11
HallC67⋊C11 ⋊ AGL(1,𝔽7)
SylowC67 ⋊ C11×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ D67⋊C11
SylowC7 ⋊ C3×D67⋊C11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C67C2×C3×C11
LCSG ▷ C7×C67
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 469

Polycyclic presentation:

2,3,7,11,67|c^a=c^6,e^a=e^66,c^b=c^2,e^d=e^64

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 70);