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C13×AGL(1,𝔽5)×C47 #27132017

order12220
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C13×C47 · Schur multiplier (H2) = C1

Aliases

direct productC13×AGL(1,𝔽5)×C47

Splittings

Fitting, socle, HallC5×C13×C47 ⋊ C4
derived, SylowC5 ⋊ C4×C13×C47
HallC5×C47 ⋊ C4×C13
HallC5×C13 ⋊ C4×C47

Subgroups

subgroupG/H
center, hypercenterC13×C47AGL(1,𝔽5)
commutator, hypocenterC5C4×C13×C47
FrattiniC1G
Fitting, socleC5×C13×C47C4
prime radicalD5×C13×C47C2
cosocleD5C2×C13×C47
LCSG ▷ C5
UCSC1 ◁ C13×C47

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3055 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽5)×C13⋊C3×C47, C3×C13×AGL(1,𝔽5)×C47, C13×C47×ΓL(1,𝔽16)
maximal normal subgroup ofAGL(1,𝔽5)×C13⋊C3×C47, C3×C13×AGL(1,𝔽5)×C47
maximal quotient ofC3×C13×AGL(1,𝔽5)×C47, C13×C47×ΓL(1,𝔽16)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12220, 13);