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C13×C47⋊AGL(1,𝔽5) #27132018

order12220
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C47⋊AGL(1,𝔽5)
unambiguous semidirect productC47⋊(C13×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC5×C13×C47 ⋊ C4
derived, HallC5×C47 ⋊ C4×C13
HallC13×C47 ⋊ AGL(1,𝔽5)
HallC5×C13 ⋊ Dic47
SylowC47 ⋊ C13×AGL(1,𝔽5)
SylowC5 ⋊ C13×Dic47

Subgroups

subgroupG/H
center, hypercenterC13C47⋊AGL(1,𝔽5)
commutator, hypocenterC5×C47C4×C13
FrattiniC1G
Fitting, socleC5×C13×C47C4
prime radicalD5×C13×C47C2
cosocleD5×C47C2×C13
LCSG ▷ C5×C47
UCSC1 ◁ C13

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1261 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC13⋊C3×C47⋊AGL(1,𝔽5), C3×C13×C47⋊AGL(1,𝔽5), C13×C3⋊(C47⋊AGL(1,𝔽5))
maximal normal subgroup ofC13⋊C3×C47⋊AGL(1,𝔽5), C3×C13×C47⋊AGL(1,𝔽5)
maximal quotient ofC3×C13×C47⋊AGL(1,𝔽5), C13×C3⋊(C47⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12220, 14);