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C41×#63120⋊C3 #44544357

order31980
automorphism?
homologyAbelianization (H1) = C3×C4×C41 · Schur multiplier (H2) = C1

Aliases

direct productC41×#63120⋊C3
unambiguous semidirect product#63120⋊(C3×C41)
unambiguous semidirect product(C41×#63120)⋊C3

Splittings

Fitting, socle, HallC5×C13×C41 ⋊ C3×C4
derived, HallC5×C13 ⋊ C3×C4×C41
HallC41×#63120 ⋊ C3
HallC5×C13⋊C3×C41 ⋊ C4
HallC13⋊C3×C41 ⋊ AGL(1,𝔽5)
HallC13×C41 ⋊ C3×AGL(1,𝔽5)
Hall#63120 ⋊ C3×C41
HallC5×C41 ⋊ Dic13⋊C3
HallC5×C13⋊C3 ⋊ C4×C41
HallC13⋊C3 ⋊ AGL(1,𝔽5)×C41
SylowC13 ⋊ C3×AGL(1,𝔽5)×C41
SylowC5 ⋊ C41×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC41#63120⋊C3
commutator, hypocenterC5×C13C3×C4×C41
FrattiniC1G
Fitting, socleC5×C13×C41C3×C4
prime radicalD5×C13⋊C3×C41C2
cosocleD5×C13C2×C3×C41
LCSG ▷ C5×C13
UCSC1 ◁ C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2665

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 85);