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C23×C7⋊AGL(1,𝔽5) #11765481

order1120
isoclinismisoclinic class of C7⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC23×C7⋊AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C22×Dic7)

Splittings

Fitting, socleC23×C5×C7 ⋊ C4
derived, HallC5×C7 ⋊ C23×C4
SylowC7 ⋊ C23×AGL(1,𝔽5)
SylowC5 ⋊ C23×Dic7

Subgroups

subgroupG/H
center, hypercenterC23C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C23×C4
FrattiniC1G
Fitting, socleC23×C5×C7C4
prime radicalC23×C7×D5C2
cosocleC7×D5C24
LCSG ▷ C5×C7
UCSC1 ◁ C23

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 280

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C23×D7×AGL(1,𝔽5), C2×D4×C7⋊AGL(1,𝔽5), …
maximal normal subgroup ofC23×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C23×D7×AGL(1,𝔽5), C2×D4×C7⋊AGL(1,𝔽5), …
maximal quotient ofC2×D4×C7⋊AGL(1,𝔽5), C24×C7⋊AGL(1,𝔽5), #41×C7⋊AGL(1,𝔽5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 1087);