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C7×D4×AGL(1,𝔽5) #11765349

order1120
automorphism?
homologyAbelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23

Aliases

direct productC7×D4×AGL(1,𝔽5)

Splittings

FittingC5×C7×D4 ⋊ C4
HallC5×C7 ⋊ C4×D4
SylowC5 ⋊ C4×C7×D4

Subgroups

subgroupG/H
centerC2×C7C22×AGL(1,𝔽5)
commutatorC2×C5C22×C4×C7
FrattiniC2C22×C7×AGL(1,𝔽5)
FittingC5×C7×D4C4
socleC2×C5×C7C22×C4
prime radicalC7×D4×D5C2
cosocleC2×D5C23×C7
hypercenterC7×D4AGL(1,𝔽5)
hypocenterC5C4×C7×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C7 ◁ C7×D4

188 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 76 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) = 140

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×AGL(1,𝔽5)×ΓL(1,𝔽8), D4×D7×AGL(1,𝔽5), C2×C7×D4×AGL(1,𝔽5), …
maximal normal subgroup ofD4×AGL(1,𝔽5)×ΓL(1,𝔽8), D4×D7×AGL(1,𝔽5), C2×C7×D4×AGL(1,𝔽5), …
maximal quotient ofC2×C7×D4×AGL(1,𝔽5), C7×D8×AGL(1,𝔽5), C7×#65731, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 955);