Finite Group Databasebeta

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AGL(1,𝔽5)×AGL(1,𝔽43) #72276192

order36120
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C7 · Schur multiplier (H2) = C2

Aliases

direct productAGL(1,𝔽5)×AGL(1,𝔽43)

Splittings

Fitting, socle, derived, HallC5×C43 ⋊ C2×C3×C4×C7
HallAGL(1,𝔽5)×D43⋊C3 ⋊ C7
HallAGL(1,𝔽5)×D43⋊C7 ⋊ C3
HallC5×(C43⋊C3)⋊C7 ⋊ C2×C4
HallAGL(1,𝔽5)×D43 ⋊ C3×C7
HallC5×C43⋊C7 ⋊ C2×C3×C4
Hall(C43⋊C3)⋊C7 ⋊ C2×AGL(1,𝔽5)
HallC5×C43⋊C3 ⋊ C2×C4×C7
HallC43⋊C7 ⋊ C2×C3×AGL(1,𝔽5)
HallC43⋊C3 ⋊ C2×C7×AGL(1,𝔽5)
SylowC43 ⋊ C2×C3×C7×AGL(1,𝔽5)
SylowC5 ⋊ C4×AGL(1,𝔽43)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C43C2×C3×C4×C7
prime radicalD5×AGL(1,𝔽43)C2
cosocleD5×C43C22×C3×C7
LCSG ▷ C5×C43
UCSC1

128 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 215

Conjugacy classes & character table

215 conjugacy classes — view the full character table.

Relationships

holomorph ofC5×C43

GAP

Past the SmallGroups library coverage — no SmallGroups id.