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C67×C11⋊AGL(1,𝔽7) #44526273

order30954
automorphism?
homologyAbelianization (H1) = C2×C3×C67 · Schur multiplier (H2) = C1

Aliases

direct productC67×C11⋊AGL(1,𝔽7)
unambiguous semidirect productC11⋊(AGL(1,𝔽7)×C67)
unambiguous semidirect productΓL(1,𝔽8)⋊(D11×C67)
unambiguous semidirect productD77⋊(C3×C67)

Splittings

Fitting, socle, HallC7×C11×C67 ⋊ C2×C3
derived, HallC7×C11 ⋊ C2×C3×C67
HallC11×ΓL(1,𝔽8)×C67 ⋊ C2
HallC67×D77 ⋊ C3
HallΓL(1,𝔽8)×C67 ⋊ D11
HallC11×C67 ⋊ AGL(1,𝔽7)
HallC7×C67 ⋊ C3×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×C67
HallD77 ⋊ C3×C67
HallΓL(1,𝔽8) ⋊ D11×C67
SylowC11 ⋊ AGL(1,𝔽7)×C67
SylowC7 ⋊ C3×D11×C67

Subgroups

subgroupG/H
center, hypercenterC67C11⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C11C2×C3×C67
FrattiniC1G
Fitting, socleC7×C11×C67C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C67

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5159

Conjugacy classes & character table

2144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 54);