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C5×C17×AGL(1,𝔽19) #44414652

order29070
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17×AGL(1,𝔽19)
unambiguous semidirect product#4296⋊(C2×C5×C17)

Splittings

Fitting, socle, HallC5×C17×C19 ⋊ C2×C9
derived, SylowC19 ⋊ C2×C5×C9×C17
HallC5×C17×#4296 ⋊ C2
HallC5×C17×D19 ⋊ C9
HallC17×#4296 ⋊ C2×C5
HallC5×#4296 ⋊ C2×C17
HallC17×D19 ⋊ C5×C9
HallC17×C19 ⋊ C2×C5×C9
HallC5×D19 ⋊ C9×C17
Hall#4296 ⋊ C2×C5×C17
HallC5×C19 ⋊ C2×C9×C17
HallD19 ⋊ C5×C9×C17

Subgroups

subgroupG/H
center, hypercenterC5×C17AGL(1,𝔽19)
commutator, hypocenterC19C2×C5×C9×C17
FrattiniC1G
Fitting, socleC5×C17×C19C2×C9
prime radicalC5×C17×D19⋊C3C3
cosocleC19⋊C3C2×C3×C5×C17
LCSG ▷ C19
UCSC1 ◁ C5×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1615

Conjugacy classes & character table

1615 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29070, 26);