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C7×AGL(1,𝔽67) #44526280

order30954
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×AGL(1,𝔽67)
unambiguous semidirect product(D67⋊C3)⋊(C7×C11)
unambiguous semidirect product(D67⋊C11)⋊(C3×C7)
unambiguous semidirect product((C67⋊C3)⋊C11)⋊(C2×C7)
unambiguous semidirect product(C7×D67⋊C3)⋊C11

Splittings

Fitting, socle, HallC7×C67 ⋊ C2×C3×C11
derived, SylowC67 ⋊ C2×C3×C7×C11
HallC7×(C67⋊C3)⋊C11 ⋊ C2
HallC7×D67⋊C11 ⋊ C3
HallC7×C67⋊C11 ⋊ C2×C3
HallC7×D67⋊C3 ⋊ C11
Hall(C67⋊C3)⋊C11 ⋊ C2×C7
HallD67⋊C11 ⋊ C3×C7
HallC7×C67⋊C3 ⋊ C2×C11
HallC7×D67 ⋊ C3×C11
HallC67⋊C11 ⋊ C2×C3×C7
HallD67⋊C3 ⋊ C7×C11
HallC67⋊C3 ⋊ C2×C7×C11
HallD67 ⋊ C3×C7×C11

Subgroups

subgroupG/H
center, hypercenterC7AGL(1,𝔽67)
commutator, cosocle, hypocenterC67C2×C3×C7×C11
FrattiniC1G
Fitting, socleC7×C67C2×C3×C11
LCSG ▷ C67
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 469

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 61);