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AGL(1,𝔽5)×#13183715 #47977650

order35340
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×#13183715

Splittings

Fitting, socle, derived, HallC5×C19×C31 ⋊ C3×C4
HallC19×AGL(1,𝔽5)×C31 ⋊ C3
HallC5×#13183715 ⋊ C4
HallAGL(1,𝔽5)×C31 ⋊ C19⋊C3
HallC19×C31 ⋊ C3×AGL(1,𝔽5)
HallC19×AGL(1,𝔽5) ⋊ C31⋊C3
HallC5×C31 ⋊ C4×C19⋊C3
HallC5×C19 ⋊ C4×C31⋊C3
SylowC31 ⋊ AGL(1,𝔽5)×C19⋊C3
SylowC19 ⋊ AGL(1,𝔽5)×C31⋊C3
SylowC5 ⋊ C4×#13183715

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C19×C31C3×C4
prime radicalD5×#13183715C2
cosocleD5×C19×C31C2×C3
LCSG ▷ C5×C19×C31
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2945

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 122);