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AGL(1,𝔽5)×C112⋊C3 #20300041

order7260
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C11

Aliases

direct productAGL(1,𝔽5)×C112⋊C3
unambiguous semidirect product(C112×AGL(1,𝔽5))⋊C3

Splittings

Fitting, socle, derived, HallC5×C112 ⋊ C3×C4
HallC112×AGL(1,𝔽5) ⋊ C3
HallC5×C112⋊C3 ⋊ C4
SylowC112 ⋊ C3×AGL(1,𝔽5)
SylowC5 ⋊ C4×C112⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C112C3×C4
LCSG ▷ C5×C112
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

215 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽5)×C112⋊C3, ΓL(1,𝔽16)×C112⋊C3, #1035×C112⋊C3, …
maximal normal subgroup ofC3×AGL(1,𝔽5)×C112⋊C3, AGL(1,𝔽5)×(C112⋊C3)⋊C5, C5×AGL(1,𝔽5)×C112⋊C3
maximal quotient ofAGL(1,𝔽5)×C112⋊C9, C3×AGL(1,𝔽5)×C112⋊C3, ΓL(1,𝔽16)×C112⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 141);