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C47×C3⋊(C11⋊AGL(1,𝔽5)) #44526658

order31020
automorphism?
homologyAbelianization (H1) = C4×C47 · Schur multiplier (H2) = C1

Aliases

direct productC47×C3⋊(C11⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C47×C11⋊AGL(1,𝔽5))
unambiguous semidirect productC11⋊(C47×ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC3×C5×C11×C47 ⋊ C4
derived, HallC3×C5×C11 ⋊ C4×C47
HallC5×C11×C47 ⋊ Dic3
HallC3×C11×C47 ⋊ AGL(1,𝔽5)
HallC3×C5×C47 ⋊ Dic11
HallC11×C47 ⋊ ΓL(1,𝔽16)
HallC5×C47 ⋊ Dic33
HallC3×C47 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C11 ⋊ Dic3×C47
HallC3×C11 ⋊ AGL(1,𝔽5)×C47
HallC3×C5 ⋊ Dic11×C47
SylowC11 ⋊ C47×ΓL(1,𝔽16)
SylowC5 ⋊ C47×Dic33
SylowC3 ⋊ C47×C11⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC47C3⋊(C11⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C11C4×C47
FrattiniC1G
Fitting, socleC3×C5×C11×C47C4
prime radicalC3×D5×C11×C47C2
cosocleC3×D5×C11C2×C47
LCSG ▷ C3×C5×C11
UCSC1 ◁ C47

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7755

Conjugacy classes & character table

3243 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 61);