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C22×C4×C7×AGL(1,𝔽5) #72218693

order2240
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C22×C42×C7 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×C4×C7×AGL(1,𝔽5)

Splittings

FittingC22×C4×C5×C7 ⋊ C4
derived, SylowC5 ⋊ C22×C42×C7
HallC5×C7 ⋊ C22×C42

Subgroups

subgroupG/H
center, hypercenterC22×C4×C7AGL(1,𝔽5)
commutator, hypocenterC5C22×C42×C7
FrattiniC2C23×C7×AGL(1,𝔽5)
FittingC22×C4×C5×C7C4
socleC23×C5×C7C2×C4
prime radicalC23×C7×D5C22
cosocleC2×D5C24×C7
LCSG ▷ C5
UCSC1 ◁ C22×C4×C7

996 conjugacy classes of subgroups; only the 552 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 552 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 ofC22×AGL(1,𝔽5)×AGL(1,𝔽29), C2×C4×D3×C7×AGL(1,𝔽5)
maximal quotient ofC22×AGL(1,𝔽5)×AGL(1,𝔽29), C2×C4×D3×C7×AGL(1,𝔽5)
automorphism group ofC3×Dic5×C29

GAP

Past the SmallGroups library coverage — no SmallGroups id.