Finite Group Databasebeta

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C11×ΓL(1,𝔽8)×C149 #46806263

order34419
automorphism?
homologyAbelianization (H1) = C3×C11×C149 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)×C149
unambiguous semidirect productC7⋊(C3×C11×C149)
unambiguous semidirect product(C7×C11)⋊(C3×C149)
unambiguous semidirect product(C7×C149)⋊(C3×C11)
unambiguous semidirect product(C7×C11×C149)⋊C3

Splittings

Fitting, socle, HallC7×C11×C149 ⋊ C3
derived, SylowC7 ⋊ C3×C11×C149
HallC7×C149 ⋊ C3×C11
HallC7×C11 ⋊ C3×C149

Subgroups

subgroupG/H
center, hypercenterC11×C149ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C3×C11×C149
FrattiniC1G
Fitting, socleC7×C11×C149C3
LCSG ▷ C7
UCSC1 ◁ C11×C149

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11473

Conjugacy classes & character table

8195 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34419, 2);