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C2×AGL(1,𝔽7)×C289 #37566165

order24276
automorphism?
homologyAbelianization (H1) = C22×C3×C289 · Schur multiplier (H2) = C2

Aliases

direct productC2×AGL(1,𝔽7)×C289
unambiguous semidirect productD7⋊(C2×C3×C289)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C289)
unambiguous semidirect product(C2×D7)⋊(C3×C289)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C289)
unambiguous semidirect product(C2×D7×C289)⋊C3

Splittings

FittingC2×C7×C289 ⋊ C2×C3
derived, SylowC7 ⋊ C22×C3×C289
HallC2×D7×C289 ⋊ C3
HallΓL(1,𝔽8)×C289 ⋊ C22
HallC7×C289 ⋊ C22×C3
HallC2×D7 ⋊ C3×C289
HallΓL(1,𝔽8) ⋊ C22×C289

Subgroups

subgroupG/H
center, hypercenterC2×C289AGL(1,𝔽7)
commutator, hypocenterC7C22×C3×C289
FrattiniC17C2×C17×AGL(1,𝔽7)
FittingC2×C7×C289C2×C3
socleC2×C7×C17C2×C3×C17
prime radicalC2×C17×AGL(1,𝔽7)C17
cosocleC7×C17C22×C3×C17
LCSG ▷ C7
UCSC1 ◁ C2×C289

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4046

Conjugacy classes & character table

4046 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24276, 18);