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C7×AGL(1,𝔽5)×C47 #20267196

order6580
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C7×C47 · Schur multiplier (H2) = C1

Aliases

direct productC7×AGL(1,𝔽5)×C47

Splittings

Fitting, socle, HallC5×C7×C47 ⋊ C4
derived, SylowC5 ⋊ C4×C7×C47
HallC5×C47 ⋊ C4×C7
HallC5×C7 ⋊ C4×C47

Subgroups

subgroupG/H
center, hypercenterC7×C47AGL(1,𝔽5)
commutator, hypocenterC5C4×C7×C47
FrattiniC1G
Fitting, socleC5×C7×C47C4
LCSG ▷ C5
UCSC1 ◁ C7×C47

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1645 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽5)×ΓL(1,𝔽8)×C47, C3×C7×AGL(1,𝔽5)×C47, C7×C47×ΓL(1,𝔽16), …
maximal normal subgroup ofAGL(1,𝔽5)×ΓL(1,𝔽8)×C47, C3×C7×AGL(1,𝔽5)×C47, C5×C7×AGL(1,𝔽5)×C47
maximal quotient ofC3×C7×AGL(1,𝔽5)×C47, C7×C47×ΓL(1,𝔽16), C7×C47×#1035, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6580, 11);