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C3×C47×C11⋊AGL(1,𝔽5) #44526642

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

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C47C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C3×C4×C47
FrattiniC1G
Fitting, socleC3×C5×C11×C47C4
prime radicalC3×D5×C11×C47C2
cosocleD5×C11C2×C3×C47
LCSG ▷ C5×C11
UCSC1 ◁ C3×C47

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7755

Conjugacy classes & character table

3525 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 45);