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AGL(1,𝔽5)×C109⋊C3 #20266906

order6540
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×C109⋊C3
unambiguous semidirect product(AGL(1,𝔽5)×C109)⋊C3

Splittings

Fitting, socle, derived, HallC5×C109 ⋊ C3×C4
HallAGL(1,𝔽5)×C109 ⋊ C3
HallC5×C109⋊C3 ⋊ C4
SylowC109 ⋊ C3×AGL(1,𝔽5)
SylowC5 ⋊ C4×C109⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C109C3×C4
LCSG ▷ C5×C109
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#11758281, C3×AGL(1,𝔽5)×C109⋊C3, ΓL(1,𝔽16)×C109⋊C3, …
maximal normal subgroup ofAGL(1,𝔽5)×#11758281, C3×AGL(1,𝔽5)×C109⋊C3, C5×AGL(1,𝔽5)×C109⋊C3
maximal quotient ofAGL(1,𝔽5)×#11758279, C3×AGL(1,𝔽5)×C109⋊C3, ΓL(1,𝔽16)×C109⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6540, 18);