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C3×#14523821⋊C5 #44544321

order31980
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×#14523821⋊C5
unambiguous semidirect product(C3×#14523821)⋊C5

Splittings

Fitting, socle, HallC3×C13×C41 ⋊ C4×C5
derived, HallC13×C41 ⋊ C3×C4×C5
HallC3×C13×C41⋊C5 ⋊ C4
HallC3×#14523821 ⋊ C5
HallC13×C41⋊C5 ⋊ C3×C4
Hall#14523821 ⋊ C3×C5
HallC3×C41⋊C5 ⋊ #261
HallC41⋊C5 ⋊ C3×#261
HallC3×C41 ⋊ C5×#261
SylowC41 ⋊ C3×C5×#261
HallC3×C13 ⋊ #4223⋊C5
SylowC13 ⋊ C3×#4223⋊C5

Subgroups

subgroupG/H
center, hypercenterC3#14523821⋊C5
commutator, hypocenterC13×C41C3×C4×C5
FrattiniC1G
Fitting, socleC3×C13×C41C4×C5
prime radicalC3×C13⋊(D41⋊C5)C2
cosocleD533C2×C3×C5
LCSG ▷ C13×C41
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1599

Conjugacy classes & character table

183 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 49);