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C3×C7×ΓL(1,𝔽8)×C11⋊C5 #37564688

order24255
automorphism?
homologyAbelianization (H1) = C32×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×ΓL(1,𝔽8)×C11⋊C5
unambiguous semidirect productC7⋊(C32×C7×C11⋊C5)
unambiguous semidirect productC11⋊(C3×C5×C7×ΓL(1,𝔽8))
unambiguous semidirect product(C3×C7)⋊(C3×C7×C11⋊C5)
unambiguous semidirect product(C3×C11)⋊(C5×C7×ΓL(1,𝔽8))
unambiguous semidirect product(C11×ΓL(1,𝔽8))⋊(C3×C5×C7)
unambiguous semidirect product(C7×C11⋊C5)⋊(C32×C7)
unambiguous semidirect product(C3×C11×ΓL(1,𝔽8))⋊(C5×C7)
unambiguous semidirect product(C3×C7×C11⋊C5)⋊(C3×C7)
unambiguous semidirect product(C3×C7×C11×ΓL(1,𝔽8))⋊C5

Splittings

Fitting, socleC3×C72×C11 ⋊ C3×C5
derivedC7×C11 ⋊ C32×C5×C7
HallC3×C7×C11×ΓL(1,𝔽8) ⋊ C5
HallC72×C11⋊C5 ⋊ C32
HallC72×C11 ⋊ C32×C5
SylowC72 ⋊ C32×C11⋊C5
SylowC11 ⋊ C3×C5×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC3×C7ΓL(1,𝔽8)×C11⋊C5
commutator, cosocle, hypocenterC7×C11C32×C5×C7
FrattiniC1G
Fitting, socleC3×C72×C11C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C3×C7

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 693

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24255, 19);