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ΓL(1,𝔽8)×D583 #37587504

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

Aliases

direct productΓL(1,𝔽8)×D583
unambiguous semidirect productC11⋊(ΓL(1,𝔽8)×D53)
unambiguous semidirect productC53⋊(ΓL(1,𝔽8)×D11)
unambiguous semidirect product(C7×D583)⋊C3

Splittings

Fitting, socle, derived, HallC7×C11×C53 ⋊ C2×C3
HallC11×ΓL(1,𝔽8)×C53 ⋊ C2
HallC7×D583 ⋊ C3
HallΓL(1,𝔽8)×C53 ⋊ D11
HallC11×C53 ⋊ C2×ΓL(1,𝔽8)
HallC7×C53 ⋊ C3×D11
HallC11×ΓL(1,𝔽8) ⋊ D53
HallC7×C11 ⋊ C3×D53
SylowC53 ⋊ ΓL(1,𝔽8)×D11
SylowC11 ⋊ ΓL(1,𝔽8)×D53
SylowC7 ⋊ C3×D583

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C53C2×C3
LCSG ▷ C7×C11×C53
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4081

Conjugacy classes & character table

1465 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24486, 20);