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ΓL(1,𝔽8)×D11×C53 #37587503

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

Aliases

direct productΓL(1,𝔽8)×D11×C53
unambiguous semidirect productC11⋊(C2×ΓL(1,𝔽8)×C53)
unambiguous semidirect product(C7×D11)⋊(C3×C53)
unambiguous semidirect product(C7×D11×C53)⋊C3

Splittings

Fitting, socle, HallC7×C11×C53 ⋊ C2×C3
derived, HallC7×C11 ⋊ C2×C3×C53
HallC11×ΓL(1,𝔽8)×C53 ⋊ C2
HallC7×D11×C53 ⋊ C3
HallC11×C53 ⋊ C2×ΓL(1,𝔽8)
HallC7×C53 ⋊ C3×D11
HallC11×ΓL(1,𝔽8) ⋊ C2×C53
HallC7×D11 ⋊ C3×C53
SylowC11 ⋊ C2×ΓL(1,𝔽8)×C53
SylowC7 ⋊ C3×D11×C53

Subgroups

subgroupG/H
center, hypercenterC53ΓL(1,𝔽8)×D11
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

1855 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24486, 19);