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C53×C11⋊AGL(1,𝔽7) #37587507

order24486
automorphism?
homologyAbelianization (H1) = C2×C3×C53 · Schur multiplier (H2) = C1

Aliases

direct productC53×C11⋊AGL(1,𝔽7)
unambiguous semidirect productC11⋊(AGL(1,𝔽7)×C53)
unambiguous semidirect productΓL(1,𝔽8)⋊(D11×C53)
unambiguous semidirect productD77⋊(C3×C53)
unambiguous semidirect product(C53×D77)⋊C3

Splittings

Fitting, socle, HallC7×C11×C53 ⋊ C2×C3
derived, HallC7×C11 ⋊ C2×C3×C53
HallC11×ΓL(1,𝔽8)×C53 ⋊ C2
HallC53×D77 ⋊ C3
HallΓL(1,𝔽8)×C53 ⋊ D11
HallC11×C53 ⋊ AGL(1,𝔽7)
HallC7×C53 ⋊ C3×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×C53
HallD77 ⋊ C3×C53
HallΓL(1,𝔽8) ⋊ D11×C53
SylowC11 ⋊ AGL(1,𝔽7)×C53
SylowC7 ⋊ C3×D11×C53

Subgroups

subgroupG/H
center, hypercenterC53C11⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C11C2×C3×C53
FrattiniC1G
Fitting, socleC7×C11×C53C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C53

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4081

Conjugacy classes & character table

1696 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24486, 23);