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C3×C11⋊(C47⋊AGL(1,𝔽5)) #44526643

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

Aliases

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

Splittings

Fitting, socle, HallC3×C5×C11×C47 ⋊ C4
derived, HallC5×C11×C47 ⋊ C3×C4
HallC3×C11×C47 ⋊ AGL(1,𝔽5)
HallC3×C5×C47 ⋊ Dic11
HallC11×C47 ⋊ C3×AGL(1,𝔽5)
HallC5×C47 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ Dic47
HallC3×C47 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C11 ⋊ C3×Dic47
SylowC47 ⋊ C3×C11⋊AGL(1,𝔽5)
HallC3×C11 ⋊ C47⋊AGL(1,𝔽5)
HallC3×C5 ⋊ Dic517
SylowC11 ⋊ C3×C47⋊AGL(1,𝔽5)
SylowC5 ⋊ C3×Dic517

Subgroups

subgroupG/H
center, hypercenterC3C11⋊(C47⋊AGL(1,𝔽5))
commutator, hypocenterC5×C11×C47C3×C4
FrattiniC1G
Fitting, socleC3×C5×C11×C47C4
prime radicalC3×D5×C11×C47C2
cosocleD5×C11×C47C2×C3
LCSG ▷ C5×C11×C47
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7755

Conjugacy classes & character table

3111 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 46);