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C2×C11×ΓL(1,𝔽8)×C37 #30685295

order17094
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C37 · Schur multiplier (H2) = C1

Aliases

direct productC2×C11×ΓL(1,𝔽8)×C37
unambiguous semidirect product(C2×C7)⋊(C3×C11×C37)
unambiguous semidirect product(C2×C7×C11)⋊(C3×C37)

Splittings

Fitting, socle, HallC2×C7×C11×C37 ⋊ C3
derived, SylowC7 ⋊ C2×C3×C11×C37
HallC7×C11×C37 ⋊ C2×C3
HallC2×C7×C37 ⋊ C3×C11
HallC7×C37 ⋊ C2×C3×C11
HallC2×C7×C11 ⋊ C3×C37
HallC7×C11 ⋊ C2×C3×C37
HallC2×C7 ⋊ C3×C11×C37

Subgroups

subgroupG/H
center, hypercenterC2×C11×C37ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C2×C3×C11×C37
FrattiniC1G
Fitting, socleC2×C7×C11×C37C3
LCSG ▷ C7
UCSC1 ◁ C2×C11×C37

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5698

Conjugacy classes & character table

4070 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C11×ΓL(1,𝔽8)×C37, C11×ΓL(1,𝔽8)×Dic37, ΓL(1,𝔽8)×C37×Dic11, …
maximal normal subgroup ofC4×C11×ΓL(1,𝔽8)×C37, C11×ΓL(1,𝔽8)×Dic37, ΓL(1,𝔽8)×C37×Dic11, …
maximal quotient ofC4×C11×ΓL(1,𝔽8)×C37, C22×C11×ΓL(1,𝔽8)×C37

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17094, 3);