Finite Group Databasebeta

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C3×C47×Dic11⋊C5 #44526616

order31020
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C47 · Schur multiplier (H2) = C1

Aliases

direct productC3×C47×Dic11⋊C5
unambiguous semidirect productDic11⋊(C3×C5×C47)
unambiguous semidirect product(C11⋊C5)⋊(C3×C4×C47)
unambiguous semidirect product(C3×Dic11)⋊(C5×C47)
unambiguous semidirect product(Dic11×C47)⋊(C3×C5)
unambiguous semidirect product(C3×Dic11×C47)⋊C5

Splittings

derived, SylowC11 ⋊ C3×C4×C5×C47
HallC3×C47×C11⋊C5 ⋊ C4
HallC3×Dic11×C47 ⋊ C5
HallC47×C11⋊C5 ⋊ C3×C4
HallDic11×C47 ⋊ C3×C5
HallC3×C11×C47 ⋊ C4×C5
HallC11×C47 ⋊ C3×C4×C5
HallC3×C11⋊C5 ⋊ C4×C47
HallC3×Dic11 ⋊ C5×C47
HallC11⋊C5 ⋊ C3×C4×C47
HallDic11 ⋊ C3×C5×C47
HallC3×C11 ⋊ C4×C5×C47

Subgroups

subgroupG/H
center, hypercenterC2×C3×C47AGL(1,𝔽11)
commutator, hypocenterC11C3×C4×C5×C47
FrattiniC2C3×C47×AGL(1,𝔽11)
Fitting, socleC2×C3×C11×C47C2×C5
prime radicalC2×C3×C47×C11⋊C5C2
cosocleC2×C11C2×C3×C5×C47
LCSG ▷ C11
UCSC1 ◁ C2×C3×C47

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6204

Conjugacy classes & character table

3102 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 19);