Finite Group Databasebeta

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C11×AGL(1,𝔽7)×C53 #37587505

order24486
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C53 · Schur multiplier (H2) = C1

Aliases

direct productC11×AGL(1,𝔽7)×C53
unambiguous semidirect productD7⋊(C3×C11×C53)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C11×C53)
unambiguous semidirect product(C11×D7)⋊(C3×C53)
unambiguous semidirect product(D7×C53)⋊(C3×C11)
unambiguous semidirect product(C11×D7×C53)⋊C3

Splittings

Fitting, socle, HallC7×C11×C53 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C11×C53
HallC11×ΓL(1,𝔽8)×C53 ⋊ C2
HallC11×D7×C53 ⋊ C3
HallΓL(1,𝔽8)×C53 ⋊ C2×C11
HallD7×C53 ⋊ C3×C11
HallC7×C53 ⋊ C2×C3×C11
HallC11×ΓL(1,𝔽8) ⋊ C2×C53
HallC11×D7 ⋊ C3×C53
HallC7×C11 ⋊ C2×C3×C53
HallΓL(1,𝔽8) ⋊ C2×C11×C53
HallD7 ⋊ C3×C11×C53

Subgroups

subgroupG/H
center, hypercenterC11×C53AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C3×C11×C53
FrattiniC1G
Fitting, socleC7×C11×C53C2×C3
LCSG ▷ C7
UCSC1 ◁ C11×C53

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4081

Conjugacy classes & character table

4081 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24486, 21);