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C3×C5×ΓL(1,𝔽8)×C37 #26042885

order11655
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C32×C5×C37 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×ΓL(1,𝔽8)×C37
unambiguous semidirect productC7⋊(C32×C5×C37)
unambiguous semidirect product(C3×C7)⋊(C3×C5×C37)
unambiguous semidirect product(C5×C7)⋊(C32×C37)
unambiguous semidirect product(C3×C5×C7)⋊(C3×C37)

Splittings

Fitting, socleC3×C5×C7×C37 ⋊ C3
derived, SylowC7 ⋊ C32×C5×C37
HallC5×C7×C37 ⋊ C32
HallC7×C37 ⋊ C32×C5
HallC5×C7 ⋊ C32×C37

Subgroups

subgroupG/H
center, hypercenterC3×C5×C37ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C32×C5×C37
FrattiniC1G
Fitting, socleC3×C5×C7×C37C3
LCSG ▷ C7
UCSC1 ◁ C3×C5×C37

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2775 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C37×AGL(1,𝔽7), C3×C5×ΓL(1,𝔽8)⋊D37, C3×C5×ΓL(1,𝔽8)×D37, …
maximal normal subgroup ofC3×C5×C37×AGL(1,𝔽7), C3×C5×ΓL(1,𝔽8)⋊D37, C3×C5×ΓL(1,𝔽8)×D37, …
maximal quotient ofC2×C3×C5×ΓL(1,𝔽8)×C37

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11655, 13);