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C7×C5⋊AGL(1,𝔽19) #26046133

order11970
automorphism?
homologyAbelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C5⋊AGL(1,𝔽19)
unambiguous semidirect productC5⋊(C7×AGL(1,𝔽19))
unambiguous semidirect product#4296⋊(C7×D5)

Splittings

Fitting, socle, HallC5×C7×C19 ⋊ C2×C9
derived, HallC5×C19 ⋊ C2×C7×C9
HallC5×C7×#4296 ⋊ C2
HallC7×D95 ⋊ C9
HallC7×#4296 ⋊ D5
HallC5×#4296 ⋊ C2×C7
HallD95 ⋊ C7×C9
Hall#4296 ⋊ C7×D5
HallC7×C19 ⋊ C9×D5
HallC5×C7 ⋊ AGL(1,𝔽19)
SylowC19 ⋊ C7×C9×D5
SylowC5 ⋊ C7×AGL(1,𝔽19)

Subgroups

subgroupG/H
center, hypercenterC7C5⋊AGL(1,𝔽19)
commutator, hypocenterC5×C19C2×C7×C9
FrattiniC1G
Fitting, socleC5×C7×C19C2×C9
prime radicalC7×C5⋊(D19⋊C3)C3
cosocleC5×C19⋊C3C2×C3×C7
LCSG ▷ C5×C19
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

287 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×D5×AGL(1,𝔽19), D7×C5⋊AGL(1,𝔽19), (C5⋊AGL(1,𝔽19))⋊D7, …
maximal normal subgroup ofC7×D5×AGL(1,𝔽19), D7×C5⋊AGL(1,𝔽19), (C5⋊AGL(1,𝔽19))⋊D7, …
maximal quotient ofC7×#4296⋊Dic5, C2×C7×C5⋊AGL(1,𝔽19)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 62);