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ΓL(1,𝔽8)2×C11⋊C5 #37564687

order24255
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productΓL(1,𝔽8)2×C11⋊C5
unambiguous semidirect productC11⋊(C5×ΓL(1,𝔽8)2)
unambiguous semidirect product(C7×ΓL(1,𝔽8))⋊(C3×C11⋊C5)
unambiguous semidirect product#3861⋊(C3×C11⋊C5)
unambiguous semidirect product#3862⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×ΓL(1,𝔽8))⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(C11×ΓL(1,𝔽8)2)⋊C5
unambiguous semidirect product(C7×ΓL(1,𝔽8)×C11⋊C5)⋊C3
unambiguous semidirect product(C11⋊C5×#3861)⋊C3
unambiguous semidirect product(C11⋊C5×#3862)⋊C3

Splittings

Fitting, socle, derived, HallC72×C11 ⋊ C32×C5
HallC11×ΓL(1,𝔽8)2 ⋊ C5
HallC72×C11⋊C5 ⋊ C32
SylowC72 ⋊ C32×C11⋊C5
SylowC11 ⋊ C5×ΓL(1,𝔽8)2

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC72×C11C32×C5
LCSG ▷ C72×C11
UCSC1

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 231

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24255, 18);