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C11⋊(C47⋊AGL(1,𝔽5)) #23780287

order10340
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC11⋊(C47⋊AGL(1,𝔽5))
unambiguous semidirect productC47⋊(C11⋊AGL(1,𝔽5))

Splittings

Fitting, socle, derived, HallC5×C11×C47 ⋊ C4
HallC11×C47 ⋊ AGL(1,𝔽5)
HallC5×C47 ⋊ Dic11
HallC5×C11 ⋊ Dic47
SylowC47 ⋊ C11⋊AGL(1,𝔽5)
SylowC11 ⋊ C47⋊AGL(1,𝔽5)
SylowC5 ⋊ Dic517

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C11×C47C4
prime radical, cosocleD5×C11×C47C2
LCSG ▷ C5×C11×C47
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,5,11,47|a^2=b,c^a=c^2,d^a=d^10,e^a=e^46,c^b=c^4

Conjugacy classes & character table

1037 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C11⋊(C47⋊AGL(1,𝔽5)), C3⋊(C11⋊(C47⋊AGL(1,𝔽5)))
maximal normal subgroup ofC3×C11⋊(C47⋊AGL(1,𝔽5))
maximal quotient ofC3×C11⋊(C47⋊AGL(1,𝔽5)), C3⋊(C11⋊(C47⋊AGL(1,𝔽5)))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10340, 23);