Finite Group Databasebeta

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C42×C5×AGL(1,𝔽7) #72219077

order3360
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C3×C42×C5 · Schur multiplier (H2) = C22×C4

Aliases

direct productC42×C5×AGL(1,𝔽7)

Splittings

FittingC42×C5×C7 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C42×C5
HallC42×C5×D7 ⋊ C3
HallC42×D7 ⋊ C3×C5
HallC5×ΓL(1,𝔽8) ⋊ C2×C42
HallC5×C7 ⋊ C2×C3×C42
HallΓL(1,𝔽8) ⋊ C2×C42×C5

Subgroups

subgroupG/H
center, hypercenterC42×C5AGL(1,𝔽7)
commutator, hypocenterC7C2×C3×C42×C5
FrattiniC22C22×C5×AGL(1,𝔽7)
FittingC42×C5×C7C2×C3
socleC22×C5×C7C23×C3
prime radicalC22×C5×AGL(1,𝔽7)C22
cosocleC22×C7C23×C3×C5
LCSG ▷ C7
UCSC1 ◁ C42×C5

432 conjugacy classes of subgroups; only the 246 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 246 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC4×C5×AGL(1,𝔽5)×AGL(1,𝔽7)
maximal quotient ofC4×C5×AGL(1,𝔽5)×AGL(1,𝔽7)

GAP

Past the SmallGroups library coverage — no SmallGroups id.