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AGL(1,𝔽7)×C67⋊C11 #44526285

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

Aliases

direct productAGL(1,𝔽7)×C67⋊C11
unambiguous semidirect productD7⋊(C3×C67⋊C11)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C67⋊C11)
unambiguous semidirect product(AGL(1,𝔽7)×C67)⋊C11

Splittings

Fitting, socle, derived, HallC7×C67 ⋊ C2×C3×C11
HallΓL(1,𝔽8)×C67⋊C11 ⋊ C2
HallD7×C67⋊C11 ⋊ C3
HallC7×C67⋊C11 ⋊ C2×C3
HallAGL(1,𝔽7)×C67 ⋊ C11
HallΓL(1,𝔽8)×C67 ⋊ C2×C11
HallD7×C67 ⋊ C3×C11
SylowC67 ⋊ C11×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C2×C67⋊C11
HallD7 ⋊ C3×C67⋊C11
SylowC7 ⋊ C2×C3×C67⋊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

Conjugacy classes & character table

119 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 66);