Finite Group Databasebeta

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C2×C7×C5⋊AGL(1,𝔽19) #37561234

order23940
automorphism?
homologyAbelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C5⋊AGL(1,𝔽19)
unambiguous semidirect product(C2×C5)⋊(C7×AGL(1,𝔽19))
unambiguous semidirect product(C2×#4296)⋊(C7×D5)

Splittings

Fitting, socleC2×C5×C7×C19 ⋊ C2×C9
derived, HallC5×C19 ⋊ C22×C7×C9
HallC5×C7×#4296 ⋊ C22
HallC2×C7×D95 ⋊ C9
HallC7×#4296 ⋊ C2×D5
HallC5×#4296 ⋊ C22×C7
HallC5×C7×C19 ⋊ C22×C9
HallC2×D95 ⋊ C7×C9
Hall#4296 ⋊ C2×C7×D5
HallC7×C19 ⋊ C2×C9×D5
HallC5×C7 ⋊ C2×AGL(1,𝔽19)
SylowC19 ⋊ C2×C7×C9×D5
SylowC5 ⋊ C2×C7×AGL(1,𝔽19)

Subgroups

subgroupG/H
center, hypercenterC2×C7C5⋊AGL(1,𝔽19)
commutator, hypocenterC5×C19C22×C7×C9
FrattiniC1G
Fitting, socleC2×C5×C7×C19C2×C9
prime radicalC2×C7×C5⋊(D19⋊C3)C3
cosocleC5×C19⋊C3C22×C3×C7
LCSG ▷ C5×C19
UCSC1 ◁ C2×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1330

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 366);