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AGL(1,𝔽5)×#63270 #19129745

order5460
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×#63270

Splittings

Fitting, socle, derived, HallC5×C7×C13 ⋊ C3×C4
HallC7×C13×AGL(1,𝔽5) ⋊ C3
HallC5×#63270 ⋊ C4
HallC13×AGL(1,𝔽5) ⋊ ΓL(1,𝔽8)
HallC7×AGL(1,𝔽5) ⋊ C13⋊C3
HallC7×C13 ⋊ C3×AGL(1,𝔽5)
HallC5×C13 ⋊ C4×ΓL(1,𝔽8)
HallC5×C7 ⋊ C4×C13⋊C3
SylowC13 ⋊ AGL(1,𝔽5)×ΓL(1,𝔽8)
SylowC7 ⋊ AGL(1,𝔽5)×C13⋊C3
SylowC5 ⋊ C4×#63270

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C13C3×C4
LCSG ▷ C5×C7×C13
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×ΓL(1,𝔽8)×C13⋊C3, C3×AGL(1,𝔽5)×#63270, ΓL(1,𝔽16)×#63270, …
maximal normal subgroup ofAGL(1,𝔽5)×ΓL(1,𝔽8)×C13⋊C3, C3×AGL(1,𝔽5)×#63270, C5×AGL(1,𝔽5)×#63270, …
maximal quotient ofAGL(1,𝔽5)×#11717941, C3×AGL(1,𝔽5)×#63270, ΓL(1,𝔽16)×#63270, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 87);