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C5×C11×ΓL(1,𝔽8)2 #37564691

order24255
automorphism?
homologyAbelianization (H1) = C32×C5×C11 · Schur multiplier (H2) = C3

Aliases

direct productC5×C11×ΓL(1,𝔽8)2
unambiguous semidirect product(C7×ΓL(1,𝔽8))⋊(C3×C5×C11)
unambiguous semidirect product#3861⋊(C3×C5×C11)
unambiguous semidirect product#3862⋊(C3×C5×C11)
unambiguous semidirect product(C5×C7×ΓL(1,𝔽8))⋊(C3×C11)
unambiguous semidirect product(C5×#3861)⋊(C3×C11)
unambiguous semidirect product(C5×#3862)⋊(C3×C11)
unambiguous semidirect product(C5×C11×#3862)⋊C3
unambiguous semidirect product(C5×C7×C11×ΓL(1,𝔽8))⋊C3
unambiguous semidirect product(C5×C11×#3861)⋊C3

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C32
derived, SylowC72 ⋊ C32×C5×C11
HallC72×C11 ⋊ C32×C5
HallC5×C72 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11ΓL(1,𝔽8)2
commutator, cosocle, hypocenterC72C32×C5×C11
FrattiniC1G
Fitting, socleC5×C72×C11C32
LCSG ▷ C72
UCSC1 ◁ C5×C11

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1155

Conjugacy classes & character table

1375 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24255, 22);